JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \( \frac{\pi}{2}<\theta<\pi \) and \( cot\theta=-\frac{1}{2\sqrt{2}} \). Then the value of \( sin(\frac{15\theta}{2})(cos8\theta+sin8\theta)+cos(\frac{15\theta}{2})(cos8\theta-sin8\theta) \) is equal to:
- A \( \frac{1-\sqrt{2}}{\sqrt{3}} \)
- B \( -\frac{\sqrt{2}}{\sqrt{3}} \)
- C \( \frac{\sqrt{2}-1}{\sqrt{3}} \)
- D \( \frac{\sqrt{2}}{\sqrt{3}} \)
Answer & Solution
Correct Answer
(A) \( \frac{1-\sqrt{2}}{\sqrt{3}} \)
Step-by-step Solution
Detailed explanation
\(\frac{\pi}{2}<\theta<\pi\) and \(\cot \theta=-\frac{1}{2 \sqrt{2}}\) \(\Rightarrow \sin \left(\frac{15 \theta}{2}\right)(\cos 8 \theta+\sin 8 \theta)\) \(+\cos \left(\frac{15 \theta}{2}\right)(\cos 8 \theta-\sin 8 \theta)\)…
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