Question

If \(\sin\theta \sin(60^\circ-\theta)\sin(60^\circ+\theta)=\dfrac18\), then \(\cos6\theta=\)

• A. \(\dfrac{\sqrt3}{2}\)
• B. \(\dfrac12\)
• C. \(\dfrac1{\sqrt2}\)
• D. \(0\)

Hint:

Memorize: \[ \sin3x=4\sin x\sin(60^\circ+x)\sin(60^\circ-x). \] It appears frequently in competitive examinations.

Answer 1

The Correct Option is B