Question

What is `cot theta + tan ^3 theta` in terms of `sintheta`?

Answer 1

`cottheta+tan^3theta`
`=costheta/sintheta+sin^3theta/cos^3theta`
`=(cos^4theta+sin^4theta)/(sintheta*cos^3theta`
`=((cos^2theta+sin^2theta)^2-2sin^2thetacos^2theta)/(sintheta(1-sin^2theta)^(3/2)`
`=(1-2sin^2theta(1-sin^2theta))/(sintheta(1-sin^2theta)^(3/2)`