Math Help - Trigonometry Identities

1. Trigonometry Identities

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 (;

2. Originally Posted by SniperMarksman
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 $= \frac{\tan x}{1 + \cos x} + \frac{\tan x}{1 - \cos x}$

$= \frac{\tan x (1 - \cos x) + \tan x (1 + \cos x)}{(1 + \cos x) (1 - \cos x)}$

Numerator: Substitute $\tan x = \frac{\sin x}{\cos x}$ and expand.

Denominator: Note the $(1 + \cos x) (1 - \cos x) = 1 - \cos^2 x = \sin^2 x$.

Continue simplifying until recognise that you've clearly got the RHS.

3. O.o alright, thanks =D

4. Angel (BestSolution)

5. Originally Posted by Angel
I will add however that the RHS is equivalent to $\frac{2}{\cos x \sin x}$ ....