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Question

tanA1cotA+cotA1tanA=1+secAcosecA

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Solution

tanA1cotA+cotA1tanA=1+secAcscA
Taking L.H.S.-
tanA1cotA+cotA1tanA
=tanA1(1tanA)+(1tanA)1tanA
=tan2AtanA1+1tanA(1tanA)
=1tan3AtanA(1tanA)
=(1tanA)(1+tanA+tan2A)tanA(1tanA)(a3b3=(ab)(a2+ab+b2))
=sec2A+tanAtanA(1+tan2A=sec2A)
=1+sec2AtanA
=1+1cosAsinA
=1+secAcscA
= R.H.S.
Hence proved.

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