Question

How do you verify the identity `(1+tantheta)/(sintheta+costheta)=sectheta`?

Answer 1

`sec theta = (1 + tan theta) / (sin theta + cos theta)`

Explanation:

`sec theta = 1/ cos theta`

`color(white)(sec theta) = 1/ cos theta * (1+tan theta)/(tan theta + 1)`

`color(white)(sec theta) = (1+tan theta)/(cos theta (tan theta + 1))`

`color(white)(sec theta) = (1+tan theta)/(cos theta (sin theta / cos theta + 1))`

`color(white)(sec theta) = (1 + tan theta) / (sin theta + cos theta)`