# HELP establish Trig Identity: 1-2cos^2 theta/ sin theta cos theta...?

Start with the left side until it equals the right side. Please show ALL work/steps, my algebra is a little rusty and I need to remember what I can and can't do. thanks!

1-2cos^2 theta/ sin theta cos theta = tan theta - cot theta

or written to see easier:

1 - 2cos^2(x) / sin(x) cos(x) = tan(x) - cot(x)

### 1 Answer

- az_lenderLv 77 years agoFavorite Answer
The main part of your algebra that needs repair has to do with

"order of operations" - look this up in Wikipedia.

The identity is FALSE the way you typed it,

but what you meant was

[1 - 2 cos^2(x)] / [sin(x) cos(x)] = tan(x) - cot(x)

Since 1 = sin^2(x) + cos^2(x), the following is equivalent to the line above:

[ sin^2(x) - cos^2(x) ] / [sin(x) cos(x)] = tan(x) - cot(x)

Then separate the two terms of the numerator:

sin^2(x)/[sin(x)cos(x)] - cos^2(x)/[sin(x)cot(x)] = tan(x) - cot(x)

and reduce the fractions:

sin(x)/cos(x) - cos(x)/sin(x) = tan(x) - cot(x)

But now it's perfectly clear that the LHS equals the RHS.