Question

Question #4acb5

Answer 1

I'm assuming you want me to prove:

`sinx/(cscx - cotx) = 1 + cosx`

We rewrite in terms of sine and cosine.

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

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

`sin^2x/(1 - cosx) = 1 + cosx`

Now recall that `sin^2x+ cos^2x = 1`:

`(1 - cos^2x)/(1 - cosx) = 1 + cosx`

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

`1 + cosx = 1 + cosx`

Proved.

Hopefully this helps!