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Question

Prove that : (sinA+cosecA)2+(cosA+secA)2=7+tan2A+cot2A.

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Solution

L.H.S.
(sinA+cosecA)2+(cosA+secA)2

=sin2A+cosec2A+2sinAcosecA+cos2A+sec2A+2cosAsecA

=1+2+2+1+tan2A+1+cot2A

=7+tan2A+cot2A = R.H.S.

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