Question

How do you simplify the following expression to a single trigonometric function? `sinx/(1-cosx) -cscx`

Answer 1

`cotx`

Explanation:

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

`(cosx-(1-sin^2x))/(sinx(1-cosx))`

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

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

`= cosx/sinx`

`= cotx`