Question

Prove (sinx/1-cosx)=cscx+cotx ?

Answer 1

See Below

Explanation:

Left Hand Side:
`=sin x/(1-cos x)((1+cos x)/(1+cos x))`-multiply by the conjugate

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

`=sin x / sin^2 x + ( sin x cos x )/ sin ^2 x`-use property `sin^2x + cos^2 x =1`

`=1/ sin x + cos x / sin x`-simply

`=csc x + cot x`

`=` Right Hand Side