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Prove the following identity, where the angle involved is acute angle for which the expressions are defined.


using the identity cosec2A=1+cot2A.

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Answer is....

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cosA-sinA+1/cosA +sinA-1 = cosecA+cotA

Use the formula cot^2A-cosec^2A

LHS-   cosA-sinA+1/cosA+sinA-1

divide by sinA on both numerator and denominator

cosA/sinA-sinA/sinA+1/sinA /cosA/sinA-sinA/sinA+1/sinA


at the place of 1 put above formula


now put it in a^2-b^2 =(a+b)(a-b)


now common taking from numerator


Hence it prove cotA+cosecA

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