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Question

Prove that : cosecAcotA=1cosA1+cosA

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Solution

wehavecosecAcotA=1cosA1+cosANowL.H.S=(cosecAcotA)=(1sinAcosAsinA)=(1cosAsinA)2=(1cosA)2sin2A=(1cosA)(1cosA)1cos2A=(1cosA)(1cosA)(1+cosA)(1cosA)=1cosA1+cosA=R.H.SHence,L.H.S=R.H.Sproved.

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