Question

Add or subtract? Simplify your answer if possible. Leave your answer in terms of sin theta and/or cos theta sin theta + 1/cos theta

`sin theta + 1/cos theta`

Answer 1

Let

`E(theta) = sintheta+1/costheta`

`E(theta) = (sinthetacostheta+1)/costheta`

This form is already in terms of `sintheta` and `costheta`, but let's continue anyway.

Recognizing that `1` is nothing more than `sin^2theta+cos^2theta`, we have

`E(theta) = (sin^2theta+sinthetacostheta+cos^2theta)/costheta`

We know that

`a^3-b^3=(a-b)(a^2+ab+b^2) => a^2+ab+b^2=(a^3-b^3)/(a-b)`

`E(theta) = ((sin^3theta-cos^3theta)/(sintheta-costheta))/costheta=(sin^3theta-cos^3theta)/(sinthetacostheta-cos^2theta)`

This is another possible answer.