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Question

Prove that : sinAcotA+cossecA=2+sinACotAcosecA

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Solution

To prove,
sinAcotA+cosecA=2+sinAcotAcosecA
sinAcotA+cosecAsinAcotAcosecA=2
Now,
LHS
sinAcotA+cosecAsinAcotAcosecA
=sinAcosecA+cotA+sinAcosecAcotA

=sinA[1cosecA+cotA+1cosecAcotA]

=sinA[cosecAcotA+cosecA+cotAcosec2Acot2A]

=sinA(2cosecA)
=2 = RHS

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