I was doing an advance reading on trigonometry (identities, specifically) when I encountered these problems on verification:

$\displaystyle

(tan^3 x + sin x sec x -sin x cos x)/(sec x - cos x) = tan x sec x + sin x

$

$\displaystyle

(1 + sin 2B + cos 2B)/(1 + sin 2B - cos 2B) = cot B

$

$\displaystyle

(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos 3x + cos 5x + cos 7x) = tan 4x

$

I'll try to edit this when I come up with answers. Thanks for those who will help!