Question

Let \(\frac{\pi}{2}<x<\pi\) be such that \(\cot x=\frac{-5}{\sqrt{11}}\). Then
\((\sin\frac{11x}{2})(\sin 6x-\cos6x)+(\cos\frac{11x}{2})(\sin 6x+\cos 6x)\)
is equal to

• A. \(\frac{\sqrt{11}-1}{2\sqrt3}\)
• B. \(\frac{\sqrt{11}+1}{2\sqrt3}\)
• C. \(\frac{\sqrt{11}+1}{3\sqrt2}\)
• D. \(\frac{\sqrt{11}-1}{3\sqrt2}\)

Answer 1

The Correct Option is B

The correct option is (B):\(\frac{\sqrt{11}+1}{2\sqrt3}\).