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Question

Solve
(sinA+cscA)2+(cosA+secA)2=7+tan2A+cot2A

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Solution

We have
(sinA+cosecA)2+(cosA+secA)2
=sin2A+cosec2A+2.sinA.cosecA+cos2A+sec2A+2cosA.secA
=1+cosec2A+2+sec2A+2[sin2θ+cos2θ=1]
=1+1+cot2A+2+1+tan2A+2[cosec2θ=1+cot2θ&sec2θ=1+tan2θ]
=7+cot2A+tan2A
Hence
(sinA+cosecA)2+(cosA+secA)2=7+cot2A+tan2A

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