SOLUTION: prove that 1/1+sinx - 1/1-sinx = -2sinx sec^2x Ive only managed to do this: LHS = 1/1+sinx - 1/1-sinx =1-sinx/1-sin^2x - 1+sinx/1-sin^2x =-2sinx/1-sin^2x =-2sinx/cos^2x

Algebra ->  Trigonometry-basics -> SOLUTION: prove that 1/1+sinx - 1/1-sinx = -2sinx sec^2x Ive only managed to do this: LHS = 1/1+sinx - 1/1-sinx =1-sinx/1-sin^2x - 1+sinx/1-sin^2x =-2sinx/1-sin^2x =-2sinx/cos^2x       Log On


   

Question 983428: prove that 1/1+sinx - 1/1-sinx = -2sinx sec^2x
Ive only managed to do this:
LHS
= 1/1+sinx - 1/1-sinx
=1-sinx/1-sin^2x - 1+sinx/1-sin^2x
=-2sinx/1-sin^2x
=-2sinx/cos^2x
and i got stuck there
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!

You are absolutely right with yours transformations.

The only thing you need to add to it is the equality

1%2Fcos%28x%29 = sec%28x%29,

which is simply the definition of  sec%28x%29,  and then

1%2Fcos%5E2%28x%29 = sec%5E2%28x%29,

which is the consequence of the definition.

Good luck !