Question

How do you solve `1/(cosx-sinx)=cosx+sinx`?

Answer 1

`x = 0 + 2pin, pi + 2pin, cosx - sinx !=0`

Explanation:

Make the equation into a product.

`1 = (cosx + sinx)(cosx - sinx)`

`1 = cos^2x - sin^2x`

Solve the pythagorean identity `sin^2x + cos^2x = 1` for `cos^2x` and substitute.

`1 = 1- sin^2x - sin^2x`

`0 = -2sin^2x`

`0 = sinx`

`x = 0 + 2pin, pi + 2pin`

Our restrictions are `cosx- sinx != 0`.

Hopefully this helps!