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Trigonometry Practice Test 2

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Question : 3 of 22

Marks: +1, -0

If

\cos x+\cos^2x=1

then what is the value of

\sin^2x+\sin^4x?

0
1
2
4
None of these

Solution:

Concept:

Use the given equation to connect

\sin^2 x

and

\cos x

.

Explanation:

Given:

\cos x+\cos^2 x=1

.

Rearrange:

\cos x=1-\cos^2 x

.

Since

\sin^2 x=1-\cos^2 x

, we get

\sin^2 x=\cos x

.

Squaring both sides gives

\sin^4 x=\cos^2 x

.

Add the two results:

\sin^2 x+\sin^4 x=\cos x+\cos^2 x

.

But

\cos x+\cos^2 x=1

.

So,

\sin^2 x+\sin^4 x=1

.

Answer:

1

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