Question

What is `costheta-tantheta*sectheta` in terms of `sintheta`?

Answer 1

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

Explanation:

`cos(theta) - tan(theta)*sec(theta)`

`=cos(theta) - sin(theta)/cos(theta) * 1/cos(theta)`

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

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

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