NIMCET 2012 — Mathematics PYQ

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Question

NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

If $\sin^2 x = 1 - \sin x$ , then $\cos^4 x + \cos^2 x$ is equal to:

Choose the correct answer:

Explanation

1. Given Equation:

\sin^2 x = 1 - \sin x

Rearrange the equation:

\sin x = 1 - \sin^2 x

2. Using Identity:

We know the fundamental trigonometric identity: $\cos^2 x = 1 - \sin^2 x$ .

Substituting this into the rearranged equation:

\sin x = \cos^2 x

3. Squaring both sides:

To find the value of $\cos^4 x$ , square both sides of the relation $\sin x = \cos^2 x$ :

(\sin x)^2 = (\cos^2 x)^2

\sin^2 x = \cos^4 x

4. Evaluating the Expression:

The expression we need to find is $\cos^4 x + \cos^2 x$ .

Substitute $\cos^4 x = \sin^2 x$ and $\cos^2 x = \sin x$ (from the steps above):

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

5. Final Substitution:

From the very first rearranged given equation ( $\sin x = 1 - \sin^2 x$ ), we can see that:

\sin^2 x + \sin x = 1

Therefore:

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

Correct Option:

(b) 1

Choose the correct answer:

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