Question

How do you simplify the expression `(1+costheta)(csctheta-cottheta)`?

Answer 1

`sin(theta)`

Explanation:

It ca be rewritten as
`(1+cos(theta))(1/sin(theta)-cos(theta)/sin(theta))`

that becomes

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