AP EAMCET · Maths · Trigonometric Ratios & Identities
\[
\sqrt{\sin ^4 x+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x}=
\]
- A \(1-\cos 2 x\)
- B \(\tan 2 x\)
- C \(\sin 2 x\)
- D \(\cos 2 x\)
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…
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