Question

Can anyone help prove this trigonometric identity?

Answer 1

Please see below.

Explanation:

`(cos^2theta-sin^2theta)/(cos^2theta+sinthetacostheta)`

= `((costheta+sintheta)(costheta-sintheta))/(costheta(costheta+sintheta))`

= `(cancel((costheta+sintheta))(costheta-sintheta))/(costhetacancel((costheta+sintheta)))`

= `(costheta-sintheta)/costheta`

= `costheta/costheta-sintheta/costheta`

= `1-tantheta`