Prove that : `(tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec – InterviewSolution

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1.	Prove that : `(tan theta)/(sectheta+1)-(tantheta)/(1-sectheta)=2cosec theta`
Answer» L.H.S `=(tantheta)/(sectheta+1)-(tantheta)/(1-sectheta)=tan theta((1)/(sectheta+1)+(1)/(sectheta-1))` `=tantheta[(sectheta-1+sectheta+1)/((sectheta-1)(sectheta+1))]= tantheta*(2sectheta)/(sec^(2)theta-1)` `=(2tanthetasectheta)/(tan^(2)theta)=(2sectheta)/(tantheta)=2xx(1)/(costheta)xx(costheta)/(sintheta)` `=(2)/(sintheta)=2"cosec"theta=R.H.S.`

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