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TS EAMCET · Maths · Functions

The period of \(\sin ^4 x+\cos ^4 x\) is

  1. A \(\frac{\pi^4}{2}\)
  2. B \(\frac{\pi^2}{2}\)
  3. C \(\frac{\pi}{4}\)
  4. D \(\frac{\pi}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

Let \(\begin{aligned} f(x) & =\sin ^4 x+\cos ^4 x \\ & =\left(\sin ^2 x+\cos ^2 x\right)^2-2 \sin ^2 x \cos ^2 x \\ & =1-\frac{1}{4} \cdot 2(\sin 2 x)^2\end{aligned}\)…