JIPMAT 2023 (QA) - If (θ) - (θ) = 0, the value of sin<sup>4</sup> (θ) + cos<sup>4</sup> (θ) is: | PYQs + Solutions

JIPMAT 2023

Geometry

Trigonometry

Easy

If $\sin (θ) - \cos (θ) = 0$ , the value of sin⁴ (θ) + cos⁴ (θ) is:

1

\frac12

\frac34

\frac14

Correct Option: 2

\sin(\theta) - \cos(\theta) = 0

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Then

\sin(\theta) = \cos(\theta)

Since

\sin^2(\theta) + \cos^2(\theta) = 1

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And

\sin(\theta) = \cos(\theta)

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Therefore

2\sin^2(\theta) = 1

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\sin^2(\theta) = \frac{1}{2}

and

\cos^2(\theta) = \frac{1}{2}

Now,

\sin^4(\theta) + \cos^4(\theta)

= (\frac{1}{2})^2 + (\frac{1}{2})^2

= \frac{1}{4} + \frac{1}{4}

= \frac{1}{2}