Question

Solve: $3(\cos \theta -\sin \theta )=1+\cos 2\theta -\sin 2\theta$.

Answer 1

$3(\cos \theta -\sin \theta )=2\cos \theta (\cos \theta -\sin \theta )$

$\therefore \cos \theta -\sin \theta =0$

or $\tan \theta =1$

$\therefore \theta =n\pi +\frac{\pi }{4}$

$\cos \theta \ne 3/2$.