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AP EAMCET · Maths · Trigonometric Ratios & Identities

\[
\sqrt{\sin ^4 x+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x}=
\]

  1. A \(1-\cos 2 x\)
  2. B \(\tan 2 x\)
  3. C \(\sin 2 x\)
  4. D \(\cos 2 x\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\cos 2 x\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { We have } \sqrt{\sin ^4+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x} \\ & \Rightarrow \sqrt{\left(2-\sin ^2(x)\right)^2}-\sqrt{\left(2-\cos ^2 x\right)^2} \\ & \Rightarrow 2-\sin ^2(x)-\left(2-\cos ^2(x)\right) \\ & =\cos ^2(x)-\sin ^2(x) \\ & =\cos 2…