Prove the following trigonometric identities: `(tantheta+sintheta)/(tantheta-sintheta)=(sectheta+1)/(sectheta-1)`

Explanation

LHS=`(tan theta+ sin theta)/(tan theta- sin theta)`


`(sin theta/costheta+sin theta)/(sintheta/cos theta-sintheta)=(sin theta+sin thetacostheta)/(sintheta+sinthetacostheta`


`(sintheta(1+cos theta))/(sintheta(1+cos theta))=(1+cos theta)/(1-cos theta)`


`(1+1/sec theta)/(1-1/sec theta)=(sectheta+1)/sectheta/(sectheta-1)/sectheta`


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