Question

Which of the following shows the simplified form of sin x/1-cos x ?

a. 1
b. sin x + tan x
c. sin x + cot x
d. csc x + cot x

Answer 1

d.
`\csc x +\cot x`

Explanation:

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