Question

What is `cottheta-csctheta+cos^2theta` in terms of `sintheta`?

Answer 1

`(sqrt(1-sin^2(theta))-1)/sin(theta) + 1-sin^2(theta)`

Explanation:

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

This could be one such way of writing the expression.