# Trigonometry Identities

• November 2nd 2008, 12:31 AM
SniperMarksman
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 (;
• November 2nd 2008, 01:32 AM
mr fantastic
Quote:

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.
• November 2nd 2008, 01:35 AM
SniperMarksman
O.o alright, thanks =D
• November 2nd 2008, 01:01 AM
Angel
Angel (BestSolution)
Still not proving..........please solve it completely please...............
• November 2nd 2008, 01:16 AM
mr fantastic
Quote:

Originally Posted by Angel
Still not proving..........please solve it completely please...............

Excuse me??

I have no intention of proving it. I've provided some direction for the OP.

I will add however that the RHS is equivalent to $\frac{2}{\cos x \sin x}$ ....
• November 2nd 2008, 06:51 AM
CaptainBlack
Quote:

Originally Posted by Angel
Still not proving..........please solve it completely please...............

You will please disist from automaticaly giving complete solutions, and not use the term "best solution" or its like in the titles of your posts.

CB