Which expression is equivalent to the following?
[tex]sin^4(x)-cos^4(x)[/tex]

This is basically calculus......

Answers

Answer 1

Step-by-step explanation:

[tex]\sin^{4}x \: - \cos^{4} x = (\sin^{2}x)^{2} - (\cos^{2}x)^{2} [/tex]

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

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

[tex] = 2\sin^{2}x - 1[/tex]

[tex] = - \cos2x[/tex]

Note: I used the identity

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

for the last step.

PS. I love proving trigonometric identities!


Related Questions

What is the surface area of the composite solid?


A rectangular prism with a length of 2 meters, width of 8 meters, and height of 2 meters. A rectangular prism with a length of 2 meters, with of 3 meters, and height of 11 meters.

Answers

Answer:

162 m^2

Step-by-step explanation:

Tops:  

 The area of the high top is 3*2 = 6

The area of the lower top is 5*2 = 10

                                                        --------

                                                           16

Bottom:

The area of the bottom is 8*2 =16

Back:

The area of the back is 2*11 = 22

Front:  

The top front is 9*2 =18

The bottom front is 2*2 =4

-------------------------------------------

                                           22

Sides

The area of the left side is

               vertical piece  11*3 =33

                 horizontal piece 5*2 = 10

                                                      -------------

                                                           43

The right side is the same = 33+10 = 43

Add them together

top+bottom+ back+front+left+right

16+16+22+22+43+43 =162 m^2

Please Help I Will Give Brainliesttt!Select the correct answer. What was the most common rating in the 26-35 age group? Average B. Good C. Excellent D. Poon​

Answers

Answer:

B. Good

Step-by-step explanation:

26-35 age group:

Excellent - 33/97

Good - 50/97

Average - 5/97

Poor - 9/97

30. Which of the following is the algebraic form for the verbal statement shown?

“13 more than the product of 4 and a number, n”


A,B,C, Or D

Answers

Answer:

Choice B

Step-by-step explanation:

4n (product of 4 and n) + 13 (13 more)

Answer:

B

Step-by-step explanation:

Each of 2 boxes of markers held 6 markers. Each of 3 packs of
rulers held 4 rulers.
How many markers and rulers were there altogether?

Answers

CORRECT ANSWER: 16 markers, 12 Rulers

EXPLANATION:
2 * 6 = 12
3 * 4 = 12

an amusement park has 350 people enter over 7 hours. what is the unit rate per hour?

Answers

Answer:

50

Step-by-step explanation:

to get the unit per hour, you have to divide the amout, which is 350, by the time, which is 7, and you get 50

Evaluate: f(2) =
Helpppp

Answers

Answer:

32

Step-by-step explanation:

Can someone please help me??

Answers

Answer:

2 2/3

Step-by-step explanation:

I used a calculator. -2.33-(-5)=2.67

Answer:

A

Step-by-step explanation:

It cannot be D, because you are subtracting the whole numbers, or B and D, because the fraction does not change.

So, if you were to solve it, you are just subtracting the whole numbers, and leaving the fraction alone. So the fraction will stay as [tex]\frac{1}{3}[/tex], while you just subtract the whole numbers.

-2+5 = 3

The answer is 3[tex]\frac{1}{3}[/tex]

(8x10^-3)+(2 x 10^-4)​

Answers

Answer:

0.0082

Step-by-step explanation:

Help me with the question​

Answers

Answer:

Step-by-step explanation:

cos 0 = 12/13. Find sin 0.
A. 5/12
B. 12/5
C. 13/12
D. 5/13

Answers

The correct value of Sine θ is 5/13

From the question given above, the following data were obtained:

Cos θ = 12/13

Sine θ =?

Next, we shall determine the opposite. This can be obtained as follow:

[tex]Cos \theta = \frac{Adjacent}{Hypothenus}\\\\Cos \theta = \frac{12}{13}[/tex]

Adjacent = 12

Hypothenus = 13

Opposite =?

Hypothenus² = Opposite² + Adjacent²

13² = Opposite² + 12²

169 = Opposite² + 144

Collect like terms

169 – 144 = Opposite²

25 = Opposite²

Take the square root of both side

Opposite = √25

Opposite = 5

Finally, we shall determine the Sine θ. This can be obtained as follow:

Opposite = 5

Hypothenus = 13

Sine θ =.?

[tex]Sine\theta = \frac{Opposite}{Hypothenus}\\\\Sine\theta = \frac{5}{13}[/tex]

Therefore, the value of Sine θ is 5/13

Learn more: https://brainly.com/question/23699928

Answer:

D. 5/13

Step-by-step explanation:

What is the absolute value of |-7|

Answers

Answer:

Step-by-step explanation:

the absolute vale of -7 is 7

Answer:

absolute value of l-7l is 7

stay safe healthy and happy.

Mrs.Taylor has cards labeled with rational numbers. *Three cards are labeled -6.35 *One card is labeled -7.53 *Two cards are labeled 8.31 What are the average numbers on the cards? *please help me on this!!*

Answers

Answer:

about 1.18 is the closest is what i got

Step-by-step explanation:

If you place a 37-foot ladder against the top of a building and the bottom of the ladder
is 22 feet from the bottom of the building, how tall is the building? Round to the
nearest tenth of a foot.

Answers

Answer:

28

Step-by-step explanation:

PLEASE PLS HELP THANK YOU

x = ___ cm

Answers

Answer:

x = 7

Step-by-step explanation:

5/(40+5) = 3/(2x+10+3)

1/9 = 3/(2x+13)

2x+13 = 3×9

2x = 27 - 13

x = 14/2

x = 7

Answer:

Step-by-step explanation:

Since they are directly proportional:

5cm -> 3cm

40cm -> y

y = 120/5

 = 24cm

2x+10 = 24

2x = 14

x = 7cm

Feel free to mark it as brainliest :D

If the weight of a package is multiplied by 3/7 the result is 42 pounds. Find the weight of the package.

Answers

Answer:

B

Step-by-step explanation:

x*3/7=42

divide 42 by 3/7: 42*7/3=98

x=98

Answer:

B) 98

Step-by-step explanation:

3/7 = 42/x

3x = 294

x = 98

What is the greatest common factor of 50, 40, and 20?

Answers

Answer:

10

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

The gcf is 10

Step-by-step explanation:

Determine the measures of A, B, C and D.

Answers

Answer:

[tex]\angle A = 32 \deg[/tex]

[tex]\angle B = 105 \deg[/tex]

[tex]\angle C = 94 \deg[/tex]

[tex]\angle D = 138 \deg[/tex]

You spin the spinner once.
What is P(3)?

Answers

Answer:

You spin the spinner once. What is P(3)? Answer : 8%.

The area of a triangle is 36 4 5 units squared and the height of the triangle is 9 1 5 units. What is the length of the triangle's base?

Answers

Answer:

I think it should be somewhere around 3528.3

Step-by-step explanation:

this is because 3645 squared minus 915 squared is 12448800 and the square root of that is 3528.3 I could be wrong though but just trying to help

5f - 2g + 3f - 4 - g

Answers

Answer:

8f-3g-4

Step-by-step explanation:

hope this helps U0U

hey! i’ll give brainliest please help

Answers

Answer:

insects adapted for stronger flight may survive in greater numbers.

D is your answer. The forth one down.

what is the volume of the square pyramid

Answers

Answer:

3710.67 mm

Step-by-step explanation:

The formula is a^2 h/3

a = 22  h = 23

First, do 22 squared which is 484.

Now do 23 divided by 3 which is 7.666666667

Now multiply 484 and 7.666666667 together to get

3710.666667 or 3710.67 mm

Help please!please ASAP

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

Use trigonometry to solve for the indicated side. Show all work
in CANVAS. Round to one decimal point (the nearest tenth).
What is the length of segment DE?
E
6
50°
D
F

Answers

Answer:

x=7.2

Step-by-step explanation:

Tan=O/A

=x/6

Tan50=x/6

×6 on both sides

6× Tan50=7.2

Answer:

DE ≈ 7.2

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan50° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{6}[/tex] ( multiply both sides by 6 )

6 × tan50° = DE , then

DE ≈ 7.2 ( to the nearest tenth )

hey! please help i’ll give brainliest

Answers

Answer:

Heyo! the answer is A since their implying it's important :)

If 2x + 4 = 10. What is the value of x

Answers

Answer:

x=3

Step-by-step explanation:

You subtract the 4 from +4 d +10 and then you left with 2x=6

Then you divide the numbers both by 2 so you are left with x=3.

Have a nice day!!!!!!!!!!

Answer:

x=3

Step-by-step explanation:

2x + 4 - 4 = 10 - 4

2x ÷ 2 = 6 ÷ 2

x = 3

nikki and dave both work as cleaners

Answers

Answer:

$80.00

Step-by-step explanation:

Find the indicated term in the sequence.

Please show steps too! Thank you.

Answers

Answer:

Value of An if n is 17 = -834

Step-by-step explanation:

Given:

A100 = 245

d = 13

n = 17

Find:

Value of An if n = 17

Computation:

An = a + (n-1)d

A100 = a + (100-1)13

245 = a + (99)17

245 = a + 1,287

a = 245 - 1,287

a = -1,042

So,

Value of An if n = 17

An = a + (n-1)d

A17 = -1,042 + (17-1)(13)

A17 = -1,042 + (16)(13)

A17 = -1,042 + 208

A17 = -834

Value of An if n is 17 = -834

Morgan invested $1,200 in an account that pays 6% annual simple interest. Morgan will not make any additional deposits or withdrawals. How much interest will Morgan earn on her investment at the end of 7 years?

Answers

Answer:

Step-by-step explanation:

Simple interest per year = $17,500 (0.0825) = $1,443.75 Simple interest = $8,662.50 Joseph Harris is considering an investment that pays 6.5 percent annually

Randy has 36 tiles.
How should he arrange them so that he has the smallest perimeter?
A.

4 by 9 rectangle
B.

3 by 12 rectangle
C.

1 by 36 rectangle
D.

6 by 6 rectangle

Answers

Answer:

Smallest perimeter setup is (6 by 6 rectangle)

Step-by-step explanation:

Given:

Total number of tile = 36

Find:

Smallest perimeter setup

Computation:

Perimeter = 2(a + b)

So,

Perimeter if (4 by 9 rectangle )

Perimeter if (4 by 9 rectangle ) = 2[4+9]

Perimeter if (4 by 9 rectangle ) = 2[13]

Perimeter if (4 by 9 rectangle ) = 26

Perimeter if (3 by 12 rectangle )

Perimeter if (3 by 12 rectangle ) = 2[3+12]

Perimeter if (3 by 12 rectangle ) = 2[15]

Perimeter if (3 by 12 rectangle ) = 30

Perimeter if (1 by 36 rectangle )

Perimeter if (1 by 36 rectangle ) = 2[1+36]

Perimeter if (1 by 36 rectangle ) = 2[37]

Perimeter if (1 by 36 rectangle ) = 74

Perimeter if (6 by 6 rectangle )

Perimeter if (6 by 6 rectangle ) = 2[6+6]

Perimeter if (6 by 6 rectangle ) = 2[12]

Perimeter if (6 by 6 rectangle ) = 24

So,

Smallest perimeter setup is (6 by 6 rectangle)

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