WBJEE · Maths · Trigonometric Ratios & Identities
If \(\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)\) then the value of \(\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)\) is
- A \(-2 \cot \theta\)
- B \(2 \cot \theta\)
- C \(2 \cos \theta\)
- D \(2 \sin \theta\)
Answer & Solution
Correct Answer
(B) \(2 \cot \theta\)
Step-by-step Solution
Detailed explanation
\(\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)\) \(=\sqrt{4 \cos ^{4} \theta+(2 \sin \theta \cos \theta)^{2}} +2 \cot \theta\left[2 \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)\right]\)…
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