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Question

Prove that (1+cotA+tanA)(sinAcosA) = secAcosec2AcosecAsec2A = sinAtanAcotAcosA

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Solution

LHS=(1+cotA+tanA)(sinAcosA)

=(1+cosAsinA+sinAcosA)(sinAcosA)

=(sinAcosA+1sinAcosA)(sinAcosA)=(sinAcosA+sin2A+cos2AsinAcosA)(sinAcosA)

=sin2AcosA+sin3A+cos2AsinAsinAcos2Acos3AcosAsin2AsinAcosA

=sin3Acos3AsinAcosA=sin2AcosAcos2AsinA

=secAcosec2AcosecAsec2A

=sinA.sinAcosAcosA.cosAsinA

=sinA.tanAcosA.cotA

=RHS

Hence proved

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