Prove that sin²α + cos²α = 1 and [tex]\frac{1}{cos^{2}\alpha }[/tex] = 1 + tan²α

$Prove That Sin + Cos = 1 And [tex]\frac{1}{cos^{2}\alpha }[/tex] = 1 + Tan$

Answers

Answer 1

Answer:

See Explanation

Step-by-step explanation:

[tex] { \sin}^{2} \alpha + { \cos}^{2} \alpha = 1 \\ \\ LHS = { \sin}^{2} \alpha + { \cos}^{2} \alpha \\ \\ = \cancel {\sin}^{2} \alpha + { 1 -\cancel{ \sin}}^{2} \alpha \\ \\ = 1 \\ \\ = RHS \\ \\ \\ \frac{1}{ { \cos}^{2} \alpha } = 1 + { \tan}^{2} \alpha \\ \\ LHS = \frac{1}{ { \cos}^{2} \alpha } \\ \\ = { \sec}^{2} \alpha \\ \\ = 1 + { \tan}^{2} \alpha \\ \\ = RHS[/tex]

Related Questions

Whoever solves this will get BRAINLIEST answer!!! Please help me out!

Answers

Answer:

x+x+x=180

3x=180

x=180/3

x=60

60 the answer is 60 hope you have a good day today!

James, Priya, and Siobhan work in a grocery store. James makes $9.00 per hour. Priya makes 40% more than James, and Siobhan makes 15% less than Priya. How much does Siobhan make per hour?

Answers

Answer:

Siobhan makes $10.71

Step-by-step explanation:

9.00 + 40% = 12.60

Priya makes $12.60.

12.6 - 15% = 10.71

Siobhan makes $10.71

Brainliest Please!!

please help me !! i beg u !!!!!!!!!!!!!!!!!!!

Answers

Answer:

D.10÷3

Step-by-step explanation:

ir you try dividing the number 10 by 3 you would get 3.333333 non-stop.

SOMEONE PLEASE HELP ME ITS URGENT!!!!

Answers

Step-by-step explanation:

i wanna help but i cant see can you copy and paste the question

Answer:

Step-by-step explanation:

y=5x-2

slope of the line is 5 because if we compare to

y=mx+b where m is the slope we see m=5

Points (0,-2), (2,8), (4,18)

slope between the points (0,-2), (2,8)

m=(y2-y1)/(x2-x1) = -2-8/0-2 = -10/-2 = 5

slope between the points (4,18), (2,8)

m=(y2-y1)/(x2-x1) = 18-8/4-2 = 10/2=5

slope between the points (4,18), (0,-2)

m=(y2-y1)/(x2-x1) = 18+2/4-0= 20/4 =5

Which of the following lengths would not create a right triangle?

A: 5, 12, 13

B: 2, 3, 4

C: 3, 4, 5

D: 6, 8, 10

Answers

Answer is (B) thanks

C I think hopefully this helps sorry if I am wrong.

PLEASE HELP NEED TO GET MY GRADE UP!!!!! ILL GIVE BRAINLST!!!!!!!

Answers

Answer:

A gardener harvested 20 tomatoes from 5 plants

Step-by-step explanation:

20 ÷ 5=4

Answer:

D) A gardener harvested 20 tomatoes from 5 planets

Step-by-step explanation:

Because:

20 ÷ 5 = 4

Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

Factsss i be scared as hell to be in front of the classroom but when we at a dance or we go out to party...we be doin all kinds of crazy shii

Answers

Answer:

that do be true tho

Step-by-step explanation:

Answer:

shii, I can throw it back and still have straight A's

Step-by-step explanation:

best of both worlds...

у = х + 4
3х — 4у = - 19

Answers

Answer:

x=3

y=7

Step-by-step explanation:

3x-4(x+4)=-19

3x-4x-16=-19

-x-16=-19

+16. +16

________

-x=-3

×-1 ×-1

______

x=3

y=3+4

y=7

In Fairbanks, Alaska, it was 13°F outside at midnight. The temperature went down 17 degrees by 6 a.m. What was the temperature, in degrees Fahrenheit, at 6 a.m.?

Answers

Answer:

13-17=-4. so -4 degrees F

Step-by-step explanation:

30 POINTSSS !!!! WILL MARK BRAINLLEST !!!!

During 16 seasons in the NHL, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number of games Gretzky played during each season:

79 82 80 80 74 84 84 79 64 78 73 78 74 86 45 53
Create a box and whisker plot for this data
Determine whether or not there are outliers present
In the form of a paragraph, explain in complete sentences the steps necessary to create the box and whisker plot and to determine whether or not outliers are present. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.

Answers

The shape is skewed to the left since there are more numbers on the right than on the left (i.e., there is a tail on the left).

All but three numbers are less than 70. Only one number is in the 60s and no numbers are in the 50s. The numbers 45 and 48 are very likely to be outliers. He might have injuries in these seasons that caused him to play fewer games than usual.

HELPPPPPPPPPPPPPPPPPPPPPPPPPPP :)

Answers

Answer:

Step-by-step explanation:

because it a custom made

Melanie used cross multiplication to correctly solve a rational equation. She found one valid solution and one extraneous solution. If 3 is the extraneous solution, which equation could she have solved?

A. The equation is 4/x-3 = x/10 because 3 makes a denominator equal zero and is not a solution of the equation derived from cross multiplying.

B. The equation is x-3/4 = 2x-6/4x because 3 makes a numerator equal zero and is a solution if the equation derived from cross multiplying.

C. The equation is 8/x^2-9 = 5/2x-6 because 3 makes the denominator equal zero and is a solution of the equation derived from cross multiplying.

D. The equation is 8/x+3 = 12/4x-3 because 3 is a solution of both the original equation and the equation derived from cross multiplying.

Answers

Answer:

The equation is 4/x-3 = x/10 because 3 makes a denominator equal zero and is not a solution of the equation derived from cross multiplying. ( A )

Step-by-step explanation:

The equation is 4/x-3 = x/10 because 3 makes a denominator equal zero and is not a solution of the equation derived from cross multiplying.

An extraneous solution is a solution that is derived from an equation that is not the original equation and when its value is plugged back into the original equation it isn't a root of the equation

determine the value of x , (5)(x)=0

Answers

Answer:

x=0

Step-by-step explanation:

The parenthesis mean that it's multiplication, so it might be easier to convert that to: 5 · x = 0. We then know that anything times zero equals zero, so 5 · 0 = 0! I hope this helps! :)

After 2 weeks, a plant is 9 centimeters tall. After 5 weeks, it has grown to 15 centimeters. If the plant grows at constant rate of change, find the following equation of the line.

Answers

Answer:

y = 2x + 5

Step-by-step explanation:

First, find the slope using rise over run, (y2 - y1) / (x2 - x1)

With this information, we can create 2 points: (2, 9) and (5, 15)

Plug in the points:

(15 - 9) / (5 - 2)

6 / 3

= 2

Plug in the slope and a point into y = mx + b, and solve for b:

y = mx + b

15 = 2(5) + b

15 = 10 + b

5 = b

Plug in the slope and b into the equation:

y = 2x + 5 is the equation of the line

where is the line or the picture

What does it mean by implied info, also can you please tell me the answer! Thanks

Look at the pic attached

Answers

Answer:

The definition of implied is something that was hinted at or suggested, but not directly stated. When a person looks at his watch and yawns multiple times as you are talking, this is an example of a situation where boredom is implied.

ba - ha = c
solve for a

Answers

Answer:

h = [tex]\frac{c}{b-h}[/tex]

Step-by-step explanation:

Given

ba - ha = c ← factor out a from each term on the left side

a(b - h) = c ← divide both sides by (b - h)

a = [tex]\frac{c}{b-h}[/tex]

Simplify the expression:

9(–4 + 4b)

Answers

Answer:

-36+36b

hope this helps

Answer:

-36+36b

Step-by-step explanation:

9×-4=-36 and 9×4b is 36b

9. What are the two forces that generate the Coriolis Effect on Earth?

heat and pressure

gravity and planetary rotation

density and salinity

gravitational pull of the Sun and Moon

Answers

Answer:

gravity and planetary rotation

Answer: Gravity and Planetary Rotation!
Hope that helps!

help me on math plz

Answers

Answer:

1/2

Step-by-step explanation:

35/70 = 1/2

Hope This Helps

What is the value of x?
A=2
B=4
C=5.5
D.7

Answers

I think D or B I believe

4) Which pair of triangles is congruent by Angle - Angle- Side?

Answers

We want to see which pair of triangles is equivalent by the Angle-Angle-Side criteria.

The correct option is 2, where we have two equal angles, and the bottom side is equal in both triangles.

The Angle-Angle-Side criteria means that if two triangles have an equal side, and the two correspondent angles also are equal, then these triangles are equivalent.

So we just need to see (by notation, not by how the triangles look like) in which ones we have two equal angles and one equal side.

That one is the second pair of triangles.

We can see that the two top angles are equal (two curves) and that the left angle in the left triangle is equal to the right angle on the other triangle (so we have two equal angles).

Also, the bottom side is equal on both triangles.

Then the angle-angle-side criteria is meet, meaning that these two triangles are equivalent.

If you want to learn more, you can read:

https://brainly.com/question/3394089

Ms. Bradley made a scatter plot with her students' individual homework averages on the x-axis and their individual average test scores on the y-axis, with both x
and y as integers between 0 and 100. She calculated the equation of the line of best fit as y=0.8z +18.
Jillian, one of Ms. Bradley's students, had a homework average of 70 and a residual of -6. What was Jillian's average test score?

Answers

Answer: 3.2z+80

Step-by-step explanation:

Please help me with this question thank you !!

Answers

The correct answer is B. 3 + 7 = 10 and (3 x 3) + 1 = 10

John is inviting himself, Lucy, and 5 of their closest friends to the party. If there are 3
3/4 cups of yogurt, how many cups of yogurt will John and the rest of the guests at the party each equally receive? PLS ANSWER. I WILL GIVE POINTS TO WHOEVER ANSWERS FIRST.

Answers

Answer:

Step-by-step explanation:

What is the slope of the graph below?

Answers

Answer:

-3/2

Step-by-step explanation:

The probability that Jim drives to work is 0.20. The probability that Jim drives to work and is late for work is 0.05. The probability that Jim is late for work, given that he bikes to work is 0.30. What is the probability that Jim is late for work, given that he drives?

Round to the nearest hundredth.

Answers

Answer:

0.45

Step-by-step explan

Anyone pls answer this plssssss

Answers

Answer:

a) x= 55°

b) x= 112°

c) x= 59°

Answer:

Step-by-step explanation:..

The ratio of boys to girls in a class is 3:4. There are 35 students in the class.
How many students are boys?

Answers

Dunno and I’m not sure very much

Answer:

Step-by-step explanation:

b : g : total

3 : 4 : 7

7u-> 35

1u->5

3u-> 15

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

Answers

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

..................................……………hi :)

Complete the equation of the line through (-9,-9)(−9,−9)left parenthesis, minus, 9, comma, minus, 9, right parenthesis and (-6,0)(−6,0)left parenthesis, minus, 6, comma, 0, right parenthesis. Use exact numbers. Y=

Answers

Answer:

The equation of the line is;

y = 3x + 18

Step-by-step explanation:

We want to write the equation of the line through (-9,-9) and (-6,0)

we start by calculating the slope of the line

m = (y2-y1)/(x2-x1) = (0+ 9)/(-6+9) = 9/3 = 3

The general equation of the line is;

y = mx + c

y = 3x + c

To get c, we use any of the points

we substitute for example -6 for x and 0 for y

0 = 3(-6) + c

c = 0 + 18 = 18

So the equation of the line is;

y = 3x + 18

Answer:

3x+18

Step-by-step explanation:

Let's find the slope:

Slope

−

(

−

)

−

(

−

)

Slope

−6−(−9)

0−(−9)

The equation is

y=3x+by, equals, 3, x, plus, b for some

bb.

Hint #22 / 3

Let's plug the point

(

−

)

(−6,0)left parenthesis, start color #11accd, minus, 6, end color #11accd, comma, start color #ed5fa6, 0, end color #ed5fa6, right parenthesis to find

bb:

(

−

)

−

=3x+b

=3(−6)+b

=−18+b

Hint #33 / 3

The equation is

y=3x+18y, equals, 3, x, plus, 18.

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