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Taking L.H.S
=(sinA+cosecA)^2+(cosA+secA)^2
=sin^2A+cosec^2A+2sinA cosecA+cos^2+sec^2A+2cosA secA
=(sin^2A+cos^2A)+2sinA×1/sinA+cosec^2A+sec^2A+2cosA×1/cosA
=1+2+cosec^2A+sec^2A+2.......(•°•sin^2A+cos^2A=1)
=5+(1+cot^2A)+(1+tan^2A) (•°•
cosec^2=1+cot^2A and sec^2A=1+tan^2A)
=7+tan^2A+cot^2A=R.H.S
°•°L.H.S=R.H.S
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