Verify: 4tan()sec() = (1+sin()/1sin()) (1sin()/1+sin())

Working with the right side,(1 + sin())/(1 - sin()) - (1 - sin())/(1 + sin())multiply the first term by (1 + sin())/(1 + sin()) and the second one by (1 - sin())/(1 - sin()). This gives(1 + sin())/(1 - sin()) (1 + sin())/(1 + sin()) = (1 + sin())^2 / (1 - sin^2()) = (1 + sin())^2 / cos^2()and(1 - sin())/(1 + sin()) (1 - sin())/(1 - sin()) = (1 - sin())^2 / (1 - sin^2()) = (1 - sin())^2 / cos^2()Now combine the fractions, expand the numerator, and simplify:(1 + sin())^2 / cos^2() - (1 - sin())^2 / cos^2() = ((1 + sin())^2 - (1 - sin())^2) / cos^2() = ((1 + 2 sin() + sin^2()) - (1 - 2 sin() + sin^2())) / cos^2() = 4 sin() / cos^2() = 4 sin()/cos() 1/cos() = 4 tan() sec()

Mathematics College

Verify: 4tan(θ)sec(θ) = (1+sin(θ)/1−sin(θ)) − (1−sin(θ)/1+sin(θ))

Answers

Answer 1

Working with the right side,

(1 + sin(θ))/(1 - sin(θ)) - (1 - sin(θ))/(1 + sin(θ))

multiply the first term by (1 + sin(θ))/(1 + sin(θ)) and the second one by (1 - sin(θ))/(1 - sin(θ)). This gives

(1 + sin(θ))/(1 - sin(θ)) • (1 + sin(θ))/(1 + sin(θ)) = (1 + sin(θ))^2 / (1 - sin^2(θ))

… = (1 + sin(θ))^2 / cos^2(θ)

and

(1 - sin(θ))/(1 + sin(θ)) • (1 - sin(θ))/(1 - sin(θ)) = (1 - sin(θ))^2 / (1 - sin^2(θ))

… = (1 - sin(θ))^2 / cos^2(θ)

Now combine the fractions, expand the numerator, and simplify:

(1 + sin(θ))^2 / cos^2(θ) - (1 - sin(θ))^2 / cos^2(θ) = ((1 + sin(θ))^2 - (1 - sin(θ))^2) / cos^2(θ)

… = ((1 + 2 sin(θ) + sin^2(θ)) - (1 - 2 sin(θ) + sin^2(θ))) / cos^2(θ)

… = 4 sin(θ) / cos^2(θ)

… = 4 • sin(θ)/cos(θ) • 1/cos(θ)

… = 4 tan(θ) sec(θ)

Related Questions

find the value of x in each case. will be posting more questions soon.

Answers

Go to photo math or cy math it will tell you the answer straight up

A stores revenue is the function y = 150x where x is the number of items they sell. Its cost function is
y = 7x + 2200 where x is the number of items they sell. How many items do they have to sell to break-
even? Show how to solve this using inverses and not the table on your calculator.
NO LINKS TO FILES OR ANYTHING LIKE THAT.

Answers

9514 1404 393

Answer:

about 15 or 16 items

Step-by-step explanation:

The break-even point is where revenue is equal to cost.

150x = 7x +2200

143x = 2200 . . . . . . . subtract 7x

x ≈ 15.38 . . . . . . . . . . divide by 143 (multiply by the inverse of 143)

When 15 items are sold, revenue doesn't quite cover costs. Costs still exceed revenue by 55. When 16 items are sold, revenue exceeds costs by 95. (I would call this the break-even point, because I prefer a slight profit over a slight loss.)

Round off to two decimal places
27.305

Answers

Answer:

20 in place value of 2

hope it helped

I need help please this isath i need my grade thx alot

Answers

Answer:

A, -475ft

Step-by-step explanation:

Answer: -475 ft

Step-by-step explanation: -95 x 5= -475

There are 6 blue marbles, 7 black marbles, 4 orange marbles, and 3 green marbles in a bag. Once a marble is drawn, it is replaced. Find
the probability of the outcome.
Find P(Blue, Orange, and then Green)

which one is the right answer:

9/1000

3/500

6/35

0

Answers

Answer:

Hello! answer 9/1000

Step-by-step explanation:

All you have to do is multiply the probability of each then you will get your answer so...

6/20 × 4/20 × 3/20 = 9/1000 So thats your probability. Hope that helps!

what is the polynomial degree for 7,8+6,5-4

Answers

Answer:

Step-by-step explanation:

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary

Answers

Answer:

5. 10 cm

6. 12 in

7. 5 mi

8. 13 cm

Step-by-step explanation:

5. 6² + 8² = x²

36 + 64 = x

36 + 64 = 100

√100 = 10

6. 15² - 9² = x²

225 - 81 = 144

√144 = 12

7. 3² + 4² = x²

9 + 16 = x

9 + 16 = 25

√25 = 5

8. 12² + 5² = x²

144 + 25 = x

144 + 25 = 169

√169 = 13

A rectangular block of wood measures 5 inches wide. Over time, the width of the block of wood will shrink by 5%. A builder lets the block of wood shrink. He wants to use it to fill a gap that measures 3.5 inches wide.
How much does the builder need to cut off the wood block so that it will fit exactly in the gap? Enter the answer in the box.

The bulder needs to cut
? Inches off the block of wood.

Answers

Answer:

1.25 inches

Step-by-step explanation:

5 - 5% is 4.75

4.75 - 3.5 is 1.25

Angle Relationships

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.

The cosine of the complimentary angle to 38°

a. 0.68
b. -0.16
c. -0.22
d. 0.62

Please select the best answer from the choices provided

Answers

Answer:

D. 0.62

Step-by-step explanation:

I calculated it logically

Can someone higher please help ?

Answers

.....................................................................................

Answer: -0.833 (repeating decimal)

Step-by-step explanation: fg(x) means plug the g(x) equation into f(x), and for gf(x) it’s vice versa:

Fg(x) = 3x^2 - 1 + 2

Gf(x) = 3(x + 2)^2 - 1

First, we should simplify gf(x) to eliminate the (x + 2)^2:

3(x^2 + 4x + 4) - 1

3x^2 + 12x + 12 - 1

3x^2 + 12x + 11

Second, simplify fg(x) by solving -1 + 2: 1

Now, we can set the two equations equal to each other and solve:

3x^2 + 1 = 3x^2 + 12x + 11 (subtract 3x^2 from each other and 1 from 11)

-10 = 12x (Divide)

-0.8333... = x

To make sure this answer is correct, plug -0.833 into the original equations and set them equal to each other:

3(-0.833)^2 + 1 = 3(-0.833)^2 + 12(-0.833] + 11

3.083 = 3.083

Describe the overall shape of this distribution. Explain your answer in complete sentences.

Answers

Answer: The histogram is skewered to the right (right-skewered)

Step-by-step explanation:

The peak veers to the left and the tail is towards the right.

The histogram given is right-skewed.

What is a histogram?

A histogram is a representation of the distribution of data with intervals.

We have,

Right-skewed and left-skewed are terms used to describe the shape of a data distribution.

A right-skewed (or positively skewed) distribution is one in which the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.

A left-skewed (or negatively skewed) distribution is the opposite of a right-skewed distribution.

In this case, the tail on the left-hand side of the graph is longer or fatter than the tail on the right-hand side.

Now,

We see that the histogram given is right-skewed because the tail on the right-hand side of the graph is longer or fatter than the tail on the left-hand side.

Thus,

The histogram given is right-skewed.

Learn more about histograms here:

https://brainly.com/question/16819077

#SPJ3

What is the lowest whole number for hypotenuse c when using the formula [tex]\sqrt{a^2+b^2}[/tex] and a = b?

Answers

9514 1404 393

Answer:

Step-by-step explanation:

If a=b, you are asking for a whole number c such that ...

c = √(a² +a²) = a√2

If 'a' is a whole number, the only whole numbers that satisfy this equation are ...

c = 0 and a = 0.

0 = 0×√2

The lowest whole number c such that c = √(a²+b²) and a=b=whole number is zero.

√2 is irrational, so there cannot be two non-zero whole numbers such that c/a=√2.

_____

Additional comment

If you allow 'a' to be irrational, then you can choose any value of 'c' that you like. Whole numbers begin at 0, so 0 is the lowest possible value of 'c'. If you don't like that one, you can choose c=1, which makes a=(√2)/2 ≈ 0.707, an irrational number. The problem statement here puts no restrictions on the values of 'a' and 'b'.

Does anyone know what 1/2*1/2*1/2*1/2 equals?
answers:
4/48
5/16
1/20736
4/12

Answers

I believe it would be 1/16.

•ω• Hewo fren!

☆☆●◉✿Answer:✿◉●☆☆

1/2*1/2*1/2*1/2= [tex]\frac{1}{2} ^{4}[/tex] Which is apparently none of these answers since it’ll be 1/16.

(Did you make a mistake with 5/16?)

☆☆●◉✿Step-by-step explanation:✿◉●☆☆

I know it is not 4/48 because that’ll be 1/12.

I know it would not be 1/20736 because the number is too small.

I know it would not be 4/12 beacuse that’ll be 1/3

And Iast but now Ieast I know it wouldn’t be 5/16 because that cannot be simplified.

HOPE I HELPED! ∧∧

→⇒brainliest please? ∑(OΔO )♥♥︎

HMP is isosceles triangle with base MP, also NP⊥OM and NM = OP Name the postulate or theorem you can use to prove NHM = OHP

Answers

Answer:

HL theorem

Step-by-step explanation:

since NP⊥OM, so, L H is a right angle.

and NM = OP as hypotenuse

HL theorem

NP is perpendicular to OM

<NHO=90°

NM =OP given

So the triangles are congruent

The point-slope equation of a line is
A. y + x - Xoyo = m
B. y= m(x - Yo)
O C. y+ mx - mxoyo
D. y-yo = m(x- xo)

Answers

Answer:

[tex]y - y_1 = m(x - x_1)[/tex]

Step-by-step explanation:

Given

A to D

Required

Which is the point slope equation

The point slope form of a coordinate pair is:

[tex]y - y_1 = m(x - x_1)[/tex]

Hence, (d) is correct

what is the angle of d

Answers

Answer:

115°

Step-by-step explanation:

65 +65 = 130

360-130= 230

230÷2= 115

(x-14) multiplied by (x+21)=0

Write down all numbers x that satisfy at least one condition.

Answers

Answer:

Step-by-step explanation:15

PLEASE help fast with attached question!! Thanks!

Answers

Answer: I thihnk it's 1x10^-2

Step-by-step explanation: This equals 0.1, and 6^-2 is equal to 0.1....the rest of the answers are either too big or too small

How many feet are in 5 yards

Answers

Answer:

15 feet

Step-by-step explanation:

Forumula: Multiply the length value by 3.

5*3= 15 feet

Hope this helped! :)

Answer:

15 feet

Step-by-step explanation:

okay so in 1 yard is 3 feet

is it is 5 yards so there is 15 feet

There are 44 rabbits. What is 44 rounded to the nearest 10?

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

44 is closer to 40 than 50 because 44-40 = 4, 50-44=6 and 4<6

what is (20)+(475)? I need it now

Answers

ur answer is going to be 495

HELP CAN SOMEONE TELL ME THE ANSWER I CANT GET A BAD GRADE.

Answers

Answer:

34.1cm^2

Step-by-step explanation:

Area of triangle = 1/2 x base x height

=1/2 x6.2 x11

=34.1cm^2

Find the dot product of u and v.

Answers

9514 1404 393

Answer:

-4

Step-by-step explanation:

The dot product is the sum of products of corresponding coefficients.

u·v = (4)(-1) +(0)(2) = -4

u·v = -4

can someone help me solve for x

Answers

Answer: Possibly -4

Step-by-step explanation:

But wait for others to check I’m not fully sure

Yeah it’s -4. Have a good day.

Multiplying polynomials
(4x+3y)(5x+y)

Answers

Answer:

20x^2 +19xy+3y^2

Step-by-step explanation:

See Image below :)

9514 1404 393

Answer:

20x² +19xy +3y²

Step-by-step explanation:

Use the distributive property.

(4x +3y)(5x +y)

= 4x(5x +y) +3y(5x +y)

= 20x² +4xy +15xy +3y²

Collect terms.

= 20x² +19xy +3y²

Plz help me well mark brainliest if you are correct!!...

Answers

Answer:

2/B

Step-by-step explanation:

The base is 9 and the height is 4.

Soren's favorite cereal is on sale. A 20-ounce box costs $4.59. A smaller, 12-ounce box costs $2.52. Complete the statements to describe which box costs less per ounce.

Answers

Answer:

The smaller box, 12 oz, costs less per oz than the larger 20 oz box.

Step-by-step explanation:

$4.59 divided by 20 = $0.2295 per oz

$2.52 divided by 12 = $0.21 per oz

What is the slope of y<-3/4x-1

Answers

Answer:

-3/4

Step-by-step explanation:

In slope-intercept form, the slope is the coefficient of x.

Some1 hurry need help

Answers

Answer:

B) (-6,9)

Step-by-step explanation:

since it's reflecting on the x-axis, the x is gonna stay the same. the y changes though. opposite of -9 is 9.

hope this helps <3

Answer:

B, (-6, 9)

Step-by-step explanation:

this is because it's like as if it was a mirror, so that is the correct answer

the value, of a 7 in the millions place, is how many times greater than the value of a 7 in the ten thousands place?

Answers

Answer:

Your answer would be 100! :)

Other Questions

2. The pitcher had 1 quarts of water. After Lena poured some of the water intoa bowl, the pitcher had') quart of water left How much water was poured inthe bowl? Can someone higher please help ? Show your work to solve me following. Will give Brainliest Underline the tense and state the kind of it:-1. he had forgotten to take his umbrella. 3. How does the location of natural resources and theclimate affect where people choose to live in Australia? What is the Ka of a solution of 0.025M formic acid, if the pH 10 pointsis 2.60? AnswersKa = 0.025Ka = 2.5x10^-4Ka = 2.8x10^-4Ka = 2.8x10^-2 plssss Write 12 important events that occur in the story of Romeo and Juliet123456789101112 Question 4The diagram represents the motion of a sound wave. The distance between points A and C is 9 meters (m), and it initially takes the wave 3 seconds (s) to travel.What will be the wavelength of the sound wave if the velocity of the wave remains constant but the pitch is tripled?A 3 meters B 6 meters 9 meters D 18 meters Describe the duties of a Rsychiatrist. what is the genetic of finger? Ill Mark you Brainiest!! Only if An Accurate and correct answer . Which of the following is not true about the lymphatic system? it brings nutrients to the tissue it drains white blood cells away from tissue it builds muscle cells it fights infection a cylindrical jar of jam has a diameter of 6cm and a height of 8 cm. if the jar is 70% full of jam how many cubic centimeters of jam are in the jar? Please answer correctly Help asap plz and thank you When Rebecca Nurse is charged, Hale is troubled. What does he intend to point out by thisallusion to the story that the Devil was once an angel?"...an hour before the Devil fell, God thought him beautiful in Heaven."O the powerful skills of deception the Devil hasO the impossibility of determining God's willOthat even beauty is no indicator of goodnessO that people sometimes change as they get older Which equations have 8 as a solution?15-n=7 n + 3 = 12 4n = 3264 : n = 8Select all the equations that have 8 as a solution.A. 15-n=7B. n + 3 = 12C. 4n = 32D. 64:n = 8 I really need help with this question!!!!!! 10OISSave for Later1Yusef is doing an experiment to find out how the amount of sunlight affects the growth of a seedling. He has three identical potscontaining grass seeds he planted at the same time. He puts them in windows that receive different amounts of sunlight each day.Every day. Yusef looks at the pots and records his observations. What is the independent variable in Yusef's experiment?OA type of soilOB type of seedling.amount of waterODamount of sunlightResetNext Question LOOK AT MY DRAWINGG :))))))))))))))))))))))))))))))))))))00 How can brain drain affect home countries?