Trig proof, I am getting a neg instead of pos.

[jrjack]

Homework Statement

[cscx/(1+cscx)] - [cscx/(1-cscx)] = 2 sec^2 x

Homework Equations

prove the left side equals the right side

The Attempt at a Solution

1. get common denominator and subtract, [cscx(1-cscx)-cscx(1+cscx)]/[(1+cscx)(1-cscx)]

2. distribute cscx in numerator [cscx-csc^2 x-cscx-csc^2 x]/
and multiply out denominator [1-csc^2 x]

3. combine like terms numerator [-2csc^2x]/
identity in denominator (cot^2 x)

4. reciprocal of cot=1/tan, then divide num/dem (-2csc^2 x)(tan^2 x)

5. change csc and tan to sin, cos [-2(1/sin^2 x)] [(sin^2 x)/(cos^2x)]

6. cross cancel and multiply -2(1/cos^2 x) or -2sec^2 x

I have checked this several times and cannot figure out why I get -2 instead of 2.

 

[Dick]

1-csc(x)^2=(-cot(x)^2), isn't it?

 

[jrjack]

Thats it. Thanks.

I knew I was overlooking something simple.