Find the solutions of the equation lying between and

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Find the solutions of the equation

(\sin x+\cos x)\sin 2x=a(\sin^3x+\cos^3x)

lying between

\frac{\pi}{2}

and

\pi

, and determine the values of

a

for which this equation has at most one solution satisfying

\frac{\pi}{2}\leq x\leq\pi