Prove that sin^4x + cos^4x= sinxcosx

Answers

Answer 1

Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

[tex]sin^4(x) + cos^4(x)[/tex]

We can rewrite this as:

[tex](sin^2(x))^2 + (cos^2(x))^2[/tex]

Now we can add and subtract cos^2(x)*sin^2(x) to get:

[tex](sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)[/tex]

We can complete squares to get:

[tex](cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2[/tex]

and we know that:

cos^2(x) + sin^2(x) = 1

then:

[tex]1 - 2*sin(x)^2*cos(x)^2[/tex]

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

[tex]1 - \frac{sin^2(2*x)}{2}[/tex]

Then the simplification is:

[tex]cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}[/tex]


Related Questions

Kinetic energy is expressed using the unit

A. Meters
b.Meters per second square
C. Joule per second
d Joule​

Answers

Answer is C I think

Answer:

C or d

Step-by-step explanation:

kinetic energy is the energy a body possesses due to its motion because it is energy, kinetic energy it expresses the unit of joules. Velocity is very similar to speed. The difference is that Velocity is the speed in the given direction

I need help ASAP i will give brainlist

Answers

Answer:

M

Step-by-step explanation:

Answer:

Point M

Step-by-step explanation:

Each line represents 0.05 so M would best represent 1/3

72,-36,18,-9 find the common ratio​

Answers

I’m not sure about the answer but there is app called Socratic can help you out

Convert: 2,640 yards miles and yards​

Answers

Answer:

1.5 miles

Step-by-step explanation:

Formula

divide the length value by 1760

Hope it helps you!

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I'm willing to help

What is the probability of choosing a clubs or a numbered card from a deck of cards? Type your answer as a fraction.

Answers

Answer:

13/52

Step-by-step explanation:

A line has a slope of -5 and includes the points (-1,r) and (-2,-2). What is the value of r?

Answers

Answer:

-7

Step-by-step explanation:

express(16^5)^1/4 in simplest radical form.

Answers

radical form: 4√16^5

Answer:

32

Step-by-step explanation:

Hello, in (16^5)^1/4, you would multiply the exponents together like this:

16^5 x 1/4= 16^5/4

The exponents multiplied make 5/4. Now you need to multiply 16 with 5/4 like this:

16 x 5/4= 80/4

80 divided by 4 is 32 so therefore, the answer is 32.

What is the equation of a circle with center (1,-4) and radius 2?
A. (x - 1)2 + (y +472 - 2
B. (x - 1)2 + (y + 4)2 - 4
C. (x + 1)2 + (y - 4) - 4
D. (x - 1)2-(y+4)2 - 4

Answers

Answer:

B. [tex](x-1)^2+(y+4)^2=4[/tex]

Step-by-step explanation:

The general equation of a circle with center (h,k) and radius r is given by :

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Substituting the given values of the center and radius into this equation we get:

[tex](x-1)^2+(y-(-4)^2=2^2[/tex]

==> remove parenthesis

[tex](x-1)^2+(y+4)^2=2^2[/tex]

==> simplify exponents

[tex](x-1)^2+(y+4)^2=4[/tex]

The equation of a circle with center (1,-4) and radius (2) is [tex](x-1)^2+(y+4)^2=4[/tex]

Learn more about the equation of a circle here : https://brainly.com/question/27248248

Rule 1: Add 7 starting from 0. Rule 2: Multiply by 2 starting from 8. Select the option that correctly shows the first 5 terms of each sequence.
Question 5 options:

First sequence: 0, 6, 12, 18, 24 and second sequence: 0, 8, 16, 32, 64

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 14, 28, 56, 112

First sequence: 14, 21, 28, 35, 42 and second sequence: 8, 16, 32, 64, 128

Answers

Answer:

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

Answer:

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

Step-by-step explanation:

PLEASE HELP! WILL GIVE BRAINLIEST! After substituting, what is the first step when evaluating 4y+9 when y=82 O Add 4 and 9. O Multiply 8 by 4. O Divide 9 by 7 O Divide 4 by 7.​

Answers

Answer:

The answer is c

Step-by-step explanation:

The diameter of a circle is 14cm. Which TWO statements are correct?

A


Answers

Answer:

(a) and (e)

Step-by-step explanation:

Given

[tex]d = 14cm[/tex]

Required

Select the true statements

First, is a statement about the area.

The area is calculated as:

[tex]Area= \pi*\frac{d^2}{4}[/tex]

So, we have:

[tex]Area= 3.14*\frac{14^2}{4}[/tex]

[tex]Area= 3.14*49[/tex]

(a) is true

Next, is a statement about the circumference.

This is calculated as:

[tex]C = \pi d[/tex]

So, we have:

[tex]C = 3.14 * 14[/tex]

(e) is true

Is 7/20 equal to 0.35

Answers

Answer:

yes it is

Step-by-step explanation:

I need some help with this math problem. I really appreciate it. thank you very much!

Margaret's savings account had $500 in it last month. This month it has $545.

Answers

Answer:

9% increase

Step-by-step explanation:

What value is missing from the table

Answers

Answer:

C. $15.75

Step-by-step explanation:

If one costs $1.05, 15 would be:

15 (1.05) = 15.75

Answer:

15.75

Step-by-step explanation:

1.05 a gallon times 15 gallons is 15.75

I NEED HELP CLICK HERE PLEASE

Answers

Answer:

A- II

B- I

C- III

D- IV

Step-by-step explanation:

Figure A is enlarged to create figure B. The ratio of the areas of A and B is 16:49.

One side of B is 5ft long. How long would the corresponding side on figure B be. Leave your answer as a fraction. (No image was provided, only the question itself.)​

Answers

Answer: [tex]\dfrac{20}{7}[/tex]

Step-by-step explanation:

Given

The ratio of the area of the similar triangles is equal to the square of the side of the corresponding sides

Suppose the corresponding side on figure A is [tex]x[/tex]

On solving

[tex]\Rightarrow \dfrac{16}{49}=[\dfrac{x}{5}]^2\\\\\Rightarrow \dfrac{x}{5}=\sqrt{\dfrac{16}{49}}\\\\\Rightarrow \dfrac{x}{5}=\dfrac{4}{7}\\\\\Rightarrow x=\dfrac{20}{7}[/tex]

One number is equal to the square of another. Find the numbers if both are positive and their sum is 306.​

Answers

Answer: 17 or -18

Step-by-step explanation:

x^2+x=306

x^2+x-306=0

(x-17)(x+18)=0

x-17=0

x=17

x+18=0

x=-18

..i think this is the right answer

A soft drink costs $1.65 and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase?

Answers

Answer: 3 refills

Step-by-step explanation:

$1.65 + 0.95 + 0.95 + 0.95 = $4.50

Using the graph, determine the coordinates of the vertex of the parabola.

Answers

I don’t know for sure, but I think the vertex is (-5, 9)

If it’s wrong, hopefully this bobcat will make your day better

A rectangular prism has a length of 9 in., a width of 4 in., and a height of 112 in.

The prism is filled with cubes that have edge lengths of 12 in.



How many cubes are needed to fill the rectangular prism?

Answers

Answer:

432

Step-by-step explanation:

Answer: 4032

Step-by-step explanation: 9x4x112 is 4032

i took the test and pls give brainiest

help please will give brainest.

Answers

Hi, you didn't add any picture or attached the info

Solve each equation.

2(−3)=14
-5(−1)=40
12(+10)=24
16(+6)=11
57(−9)=25

Answers

Answer:

jkudrhytiu4wry bui634y uiyb4uiyttui4ytui4yuityu34w ytiuyy4ty4oi8t4otiu4ioyt

Step-by-step explanation:

ryeropiutopier5uoiyturloiuy6otieruoiyluriluyrtuur6

These four numbers are plotted on a number line:

-23,58,-35,-12

Which is the correct ordering on the number line, from left to right? A . -12,-35,-23,58 B. -12,-35,58,-23 C. -23,-35,-12,58 D. -35,-23,-12,58

Answers

Answer:

D

Step-by-step explanation:

Need help

1. 15% of what number is 6?

2. 25 is 10% of what number

3. 49 is 35% of what number

4. What is 310% of 65

Thanks

Answers

Answer:

1. 40

2. 40

3. 140

4. 210.5

I tried, hope this helps :)

A rectangle with sides 11 cm and 9 cm has the same diagonal as a square.
What is the length of the side of the square.
Give your answer as a surd.​

Answers

Answer:

the length will be 9cm because a square has equal sides it not the same as the rectangle

the area of a square room is 144square metres what is the perimeter of the room​

Answers

Answer:

the answer is 48

Step-by-step explanation:

12×12=144

4×12=48

please help! what is the measure of each central angle?

Answers

Answer:

9.3

Step-by-step explanation:

The slope of the line whose equation is 2x + 5y + 1 = 0 is
0-2/5
05/2
0-1/5

Answers

Answer:

0-2/5

I think this is it ;-;


PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!

Answers

Answer:

maybe the second?

Step-by-step explanation:

Use trigonometric identities to simplify the expression.

cot(β+π)sin(β

Answers

Answer:

cosβ

Step-by-step explanation:

cot(β+π)sinβ

cot(x)=cos(x)/sin(x), so we can rewrite our expression as:

(cos(β+π)/sin(β+π)) * sinβ

sin(a+b)=sin(a)cos(b)+cos(a)sin(b), so we can rewrite our expression as:

(cos(β+π)/(sinβcosπ+cosβsinπ)) * sin(β)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b), so we can rewrite our expression as:

(cosβcosπ-sinβsinπ)/(sinβcosπ+cosβsinπ)) * sin(β)

cosπ=-1 and sinπ=0, so we can rewrite our expression as:

(-cosβ)/(-sinβ) * sin(β)

(-cosβ)/(-sinβ) * sin(β)

=(cosβ/sinβ)(sinβ)

=cosβ

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