AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\theta\) is in the third quadrant, then \(\sqrt{4 \sin ^4 \theta+\sin ^2 2 \theta}+4 \cos ^2\left(\frac{\pi}{4}-\frac{\theta}{2}\right)=\)
- A \(1+2 \sin \theta\)
- B 2
- C 1
- D \(2+4 \sin \theta\)
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(\sqrt{4 \sin ^4 \theta+\sin ^2 2 \theta} = \sqrt{4 \sin ^4 \theta+ (2 \sin \theta \cos \theta)^2}\) \(= \sqrt{4 \sin ^4 \theta+4 \sin ^2 \theta \cos ^2 \theta} = \sqrt{4 \sin ^2 \theta(\sin ^2 \theta+\cos ^2 \theta)}\) \(= \sqrt{4 \sin ^2 \theta} = |2 \sin \theta|\) Since…
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