Question

prove that
(cosec^2theta/cosec theta-1)-(cosec^2theta/cosec theta+1)=2sec^2 theta


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Answer 1

Answer:

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Answer 2

L.H.S= (cosec^2theta/cosecthetha-1)-(cosec^2theta/cosecthetha+1)

=cosec^2thetha(cosecthetha+1)-cosec^2thetha(cosecthetha-1)/cosec^2thetha-1

=cosec^2thetha(cosecthetha-cosecthetha+1+1)/cosec^2thetha-1

then formula:- cosec^2thetha-1=cot^2thetha

=cosec^2thetha*2/cot^2thetha

=2cosec^2thetha/cot^2thetha

then formula:- cosec^2thetha=1/sin^2thetha

same as:- cot^2thetha=cos^2thetha/sin^2thetha

=2*1/sin^2thetha/cos^2thetha/sin^2thetha

=2*sin^2thetha/sin^2thetha*1/cos^2thetha

formula:-1/cos^2thetha=sec^2thetha

=2sec^2thetha

L.H.S=R.H.S

proved