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san4es73 [151]
1 year ago
8

If sin A + sin^3 A = cos^2 A, prove that cos^6 A - 4cos^4 A + 8cos^2 A = 4.

Mathematics
2 answers:
ZanzabumX [31]1 year ago
6 0

Answer:

Step-by-step explanation:

sinA+sin

3

A=cos

2

A

⇒sinA[1+sin

2

A]=cos

2

A

⇒sinA[1+1−cos

2

A]=cos

2

A

squaring on both sides.

⇒sin

2

A[4+cos

4

A−4cos

2

A]=cos

4

A

⇒(1−cos

2

A)[4+cos

4

A−9cos

2

A]=cos

4

A

⇒4+cos

4

A−4cos

2

A−64cot

2

A−cos

6

A+9cos

4

A=cos

4

A

⇒

cos

6

A−4cos

4

A+8cos

2

A=4

​

Hence Prove

Sphinxa [80]1 year ago
4 0

Answer:

Step-by-step explanation:

sinA(1+sin^2A) = cos^2A

sinA(2 -cos^2A) = cos^2A

Squaring both sides,

sin^2A(4-4cos^2A +cos^4A) = cos^4A

(1-cos^2A)(4-4cos^2A +cos^4A) = cos^4A

4-4cos^2A +cos^4A-4cos^2A+4cos^4A-cos^6A = cos^4A

4 -cos^6A +4cos^4A -8cos^2A = 0

cos^6A - 4 cos^4A + 8cos^2A = 4

hence proveproven

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suter [353]

Answer:

She needs 0,75 ft of wire

Step-by-step explanation:

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2 years ago
what transformation was not done to the linear parent function f(x) to get the function (x)=-3(x+4)-7
Dominik [7]

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3 0
3 years ago
The graph of f is shown. find and interpret f(45).
Ket [755]

The function represents the number of accidents (f(x)) per 50 million miles driven as a function of the driver's age (x).

f(x)=0.4x^2-36x+1000

f(45) indicates that you have to find the value of f(x) when x=45, to do so replace the equation of the function with the value of x and solve for f(x)

\begin{gathered} f(x)=0.4x^2-36x+1000 \\ f(45)=0.4(45)^2-36\cdot45+1000 \\ f(45)=0.4\cdot2025-1620+1000 \\ f(45)=810-1620+1000 \\ f(45)=190 \end{gathered}

For x=45 years f(x)=190

f(45)=190; This value indicates that 45-year-old drivers had 190 accidents per 50 million miles driven.

8 0
1 year ago
Hevesh wants to make 2 lines of dominoes that are both 21 inches long. Each line has dominoes spaced 1 and 1/2 inches apart. How
aliya0001 [1]

Answer: 30 dominoes in total.

Step-by-step explanation:

Each line is 21 inches long.

the space between dominoes is 1 + 1/2 inches.

(assuming that the distance includes the domino itself) Now, we need at least two dominoes to see this distance,

The we have N + 1 dominoes per line, and the distance is:

N*(1 + 1/2)inches = 21 inches

If we find N, we can find the number of domineoes in each line:

N = 21/(1 + 1/2) = 14

This means that we have 14  + 1 = 15 dominoes in each line, and we have two lines, so we have 30 dominoes in total.

3 0
3 years ago
Pippa had 35 stickers.
Ivan

Answer: 3 stickers

Step-by-step explanation:

From the question, we know that Pippa's 8 friends have an equal amount of stickers, meaning that the number of stickers that Pippa gave out is a multiple of 8.

Also, we are able to know that Pippa gave as much as she can, meaning that she gave out the stickers until the number is the maximum multiple of 8.

First Five Multiple of 8 = 8, 16, 24, 32, 40

As we can see from the list, 8, 16, and 24 are all multiples of 8, but they are not the maximum number that could fit under 35 stickers. Similarly, 40 exceeds the number of stickers Pippa has. Thus, we are left with 32.

This means, Pippa gave out 32 stickers in total, and each friend got 4 stickers.

  • 32 / 8 = 4 stickers

Also, this means Pippa would keep <u>3 stickers</u> for herself.

  • 35 - 32 = 3 stickers

Hope this helps!! :)

Please let me know if you have any questions

5 0
2 years ago
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