TanA/1-cotA+cotA/1-tanA=secA.cosecA+1
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Step-by-step explanation:
LHS
=sinA/cosA÷1-cosA/sinA+cosA/sinA÷1- sinA/cosA
=sinA/cosA×sinA/sinA-cosA+cosA/sinA×cosA/cosA-sinA
=sin²A/cosA(sinA-cosA)+cos²A/sinA(cosA-sinA)
=sin²A/cosA(sinA-cosA)-cos²A/sinA(sinA-cosA)
=sin³A-cos³A/sinAcosA(sinA-cosA)
=(sinA-cosA)(sin²A+sinAcosA+cos²A)/ sinAcosA(sinA-cosA)
=1+sinAcosA/sinAcosA
=1/sinAcosA+sinAcosA/sinAcosA
=cosecAsecA+1
=RHS
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