Question

Prove 1+cos x/1-cos x = 1+ 2cos x(1+cos x)/sinˆ2 Please and thank you! (?)

The picture is just in case it wasn't clearly typed. It's question 23. Steps would be greatly appreciated.

We are using these to help us but I forget the steps.

Answer 1

`(1+cos x)/(1-cos x)`

`=>((1+cos x)(1+cos x))/((1-cos x)(1+cos x))` `color(white)(ggg)` `["multiply and divide by " 1+cosx]`

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

`=>(1+cos^2x +2cosx)/(sin^2 x)` `color(white)(wwwwwwwiwggg)` `[sin^2x+cos^2x=1]`

`=>(sin^2x +cos^2x +cos^2x +2cosx)/(sin^2 x)` `color(white)(wggg)` `[sin^2x+cos^2x=1]`

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

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