Hi I need help in proving trigonometric identities.
The qn is Prove the identity:
tan x/ 1 + cos x + tan x/1 - cos x = 2 (tan x + cot x )
Thanks (;
LHS $\displaystyle = \frac{\tan x}{1 + \cos x} + \frac{\tan x}{1 - \cos x}$
$\displaystyle = \frac{\tan x (1 - \cos x) + \tan x (1 + \cos x)}{(1 + \cos x) (1 - \cos x)}$
Numerator: Substitute $\displaystyle \tan x = \frac{\sin x}{\cos x}$ and expand.
Denominator: Note the $\displaystyle (1 + \cos x) (1 - \cos x) = 1 - \cos^2 x = \sin^2 x$.
Continue simplifying until recognise that you've clearly got the RHS.