Question

How do you express `sin^2 theta - tan theta + sec^2 theta` in terms of `cos theta`?

Answer 1

`1-cos^2theta-sqrt(1-cos^2theta)/costheta+1/cos^2theta`

Explanation:

For expressing `sin^2theta-tantheta+sec^2theta` in terms of `costheta`, let us the identities

`sin^2theta=1-cos^2theta` or `sintheta=sqrt(1-cos^2theta)` and

`tantheta=sintheta/costheta` and `sec^2theta=1/cos^2theta`,

Using these

`sin^2theta-tantheta+sec^2theta`

= `1-cos^2theta-sintheta/costheta+1/cos^2theta`

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