a) $ \cos^6x + \sin^6x = 2(\cos^8x+\sin^8x) $
b) $ 2 \sin^3 x - \cos 2x + \cos x =0 $
c) $ \cos 2x + 5 = 2 ( 2x - \cos x ) ( \sin x - \cos x) $
d) $ 8\sqrt{2} \cos^6 x + 2\sqrt{2}\sin^3 sin 3x - 6\sqrt{2}\cos^4x-1=0$
e) $\frac{1}{\tan x + \cot 2x}= \frac{\sqrt{2}(\cos x - \sin x )}{\cot x -1} $