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Question

tanA1cotA+cotA1tanA=secAcosecA+1.

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Solution

tanA1cotA+cotA1tanA=secA cosecA+1

L.H.S––––––
=tanA11tanA+cotAtanA1tanA
=tan2AtanA1+1tanA(1tanA)=1tanA1(tan2A1tanA)=1tanA1(tan3A1tanA)1tanA1(tanA1)(tan2A+1+tanAtanA)
=sec2A+tanAtanA(1+tan2A=sec2A)=sec2AtanA+1=1cos2AsinAcosA+1=1sinAcosA+1=secAcosecA+1(R.H.S)

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