# Thread: trig functions: verifying identities

1. ## trig functions: verifying identities

how would you verify SIN(X)/ 1+COS(X) + SIN(X)/1-COS(X) = 2CSC(X)

2. Originally Posted by loganmeyers
how would you verify SIN(X)/ 1+COS(X) + SIN(X)/1-COS(X) = 2CSC(X)
start with the left hand side. you are going to manipulate it until you get the right hand side.

begin by combining the fractions, then simplify

3. Originally Posted by loganmeyers
SIN(X)/ 1+COS(X) + SIN(X)/1-COS(X) = 2CSC(X)
$\frac{{\sin x}}
{{1 + \cos x}} + \frac{{\sin x}}
{{1 - \cos x}} = \sin x\left( {\frac{1}
{{1 + \cos x}} + \frac{1}
{{1 - \cos x}}} \right) = \frac{{2\sin x}}
{{\sin ^2 x}}$

Can you take it from there?