Question

Verify the identity.
sin x/1-cos x = csc x + cot x​

Answer 1

See below for proof

Explanation:

`\displaystyle (\sin x)/(1-\cos x)=(\sin x(1+\cos x))/((1-\cos x)(1+\cos x))\\\\(\sin x)/(1-\cos x)=(\sin x(1+\cos x))/(1-\cos^2 x)\\\\(\sin x)/(1-\cos x)=(\sin x(1+\cos x))/(\sin^2 x)\\\\(\sin x)/(1-\cos x)=(1+\cos x)/(\sin x)\\\\(\sin x)/(1-\cos x)=(1)/(\sin x)+(\cos x)/(\sin x)\\\\(\sin x)/(1-\cos x)=\csc x+\cot x`