JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \( \cot x=\frac{5}{12} \) for some \( x\in(\pi,\frac{3\pi}{2}) \), then \( \sin 7x(\cos\frac{13x}{2}+\sin\frac{13x}{2}) + \cos 7x(\cos\frac{13x}{2}-\sin\frac{13x}{2}) \) is equal to
- A \(\frac{4}{\sqrt{26}}\)
- B \(\frac{6}{\sqrt{26}}\)
- C \(\frac{1}{\sqrt{13}}\)
- D \(\frac{5}{\sqrt{13}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{13}}\)
Step-by-step Solution
Detailed explanation
\(\cot x=\frac{5}{12} \Rightarrow \cos x=\frac{-5}{13}=2 \cos ^2 \frac{x}{2}-1\) \(\cos \left(\frac{x}{2}\right)=-\frac{2}{\sqrt{13}}\) or \(\frac{2}{\sqrt{13}}(\) rejected \()\) \(\left\{\because \frac{x}{2} \in\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right)\right\}\)…
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