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Question

Prove that :
(1+cotA+tanA)(sinAcosA)=sinAtanAcotAcosA.

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Solution

Let
L.H.S= (1+cotA+tanA)(sinAcosA)
=(1+cosAsinA+sinAcosA)(sinAcosA)
=(sinAcosA+cos2A+sin2AsinAcosA)(sinAcosA)
=(1+sinAcosA)(sinAcosAsinAcosA)
Now,
R.H.S=sinAtanAcotAcosA
=sinAsinAcosAcosAsinAcosA
=sin2AcosAcos2AsinA
=sin3Acos3AsinAcosA
=(sinAcosA)sinAcosA(sin2A+cos2A+sinAcosA)
=(1+sinAcosA)(sinAcosA)sinAcosA
Hence,
L.H.S=R.H.S
proved

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