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Question

Prove that: (sinA+secA)2+(cosA+cosec A)2=(1+secAcosecA)2.

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Solution


LHS =(sinA+secA)2+(cosA+cosecA)2

=sin2A+cos2A+sec2A+cosec2A+2sinAcosA+2cosAsinA

=1+[1sin2Acos2A]+2[1sinAcosA]

RHS=(1+1sinAcosA)2

=1+1sin2Acos2A+2sinAcosA

LHS=RHS

Hence proved

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