Originally Posted by

**azuresonata** 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

$

Mr F says: At a glance, I'd suggest making the sustitutions $\displaystyle {\color{red}\tan x = \frac{\sin x}{\cos x}}$ and $\displaystyle {\color{red}\sec x = \frac{1}{\cos x}}$ on each side and then simplifying the resulting expressions.

$\displaystyle

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

$

Mr F says: At a glance I'd suggest substituting from the double angle formulae in the left hand side and simplifying the resulting expression.

$\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!