Question

What is `sectheta+costheta` in terms of `sintheta`?

Answer 1

Recall:
`1. sectheta=1/costheta`

To rewrite the expression in terms of `sintheta`, use the above reciprocal identity to simplify the expression:

`sectheta+costheta`

`=1/costheta+costheta`

`=(1+costheta(costheta))/costheta`

`=(1+cos^2theta)/costheta`

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

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