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Question

(cotA-cosecA)(cotA-cosecA) =1-cosA/1+cosA

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Solution

RHS=1-cosA/1+cosA
By multiplying and dividing by (1-cosA)
=(1-cosA)^2/(1-cos^2A)
=(1-cosA)^2/sin^2A
=(cosecA-cotA)^2
=(cotA-cosecA)^2
=(cotA- cosecA)( cotA- cosecA)
=LHS
proved

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