Question

Prove that sin theta/1-cos theta +tan theta /1+cos theta=sec theta*cosec theta +cot theta?

Answer 1

Please see below.

Explanation:

`sintheta/(1-costheta)+tantheta/(1+costheta)`

= `(sintheta(1+costheta))/((1-costheta)(1+costheta))+(tantheta(1-costheta))/((1+costheta)(1-costheta))`

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

= `(sintheta(1+costheta))/sin^2theta+(sintheta(1-costheta))/(costhetasin^2theta)`

= `(1+costheta)/sintheta+(1-costheta)/(costhetasintheta)`

= `1/sintheta+costheta/sintheta+1/(costhetasintheta)-1/sintheta`

= `csctheta+cottheta+secthetacsctheta-csctheta`

= `secthetacsctheta+cottheta`