Question

What is `(costheta)/3` in terms of `tantheta`?

Answer 1

`costheta/3=+-1/(3sqrt(tan^2theta+1)`

Explanation:

We know that `Sintheta/Costheta=Tantheta`
`impliesSin^2theta/cos^2theta=tan^2theta`
`impliescos^2theta=sin^2theta/tan^2theta`
Also `Sin^2theta=1-cos^2theta`

`implies cos^2theta=(1-cos^2theta)/tan^2theta`

`implies cos^2theta=1/tan^2theta-cos^2theta/tan^2theta`

`implies cos^2theta+cos^2theta/tan^2theta=1/tan^2theta`

`implies cos^2theta(1+1/tan^2theta)=1/tan^2theta`

`implies cos^2theta(1+1/tan^2theta)=1/tan^2theta`

`implies cos^2theta=(1/tan^2theta)/(1+1/tan^2theta)`

`implies cos^2theta=1/(tan^2theta+1)`

`implies costheta=+-sqrt(1/(tan^2theta+1))`

`implies costheta=+-1/sqrt(tan^2theta+1)`

`implies costheta/3=+-(1/sqrt(tan^2theta+1))/3`

`implies costheta/3=+-1/(3sqrt(tan^2theta+1)`