prove that tanQ/1 - cotQ + cotQ/1 - tanQ = 1 + tanQ + cotQ
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Step-by-step explanation:
LHS:
tanA/1-cotA + cotA/1-tanA
=(sinA/cosA)/(sinA-cosA/sinA)+(cosA/sinA)/(cosA-sinA/cosA)
=sin²A/cosA(sinA-cosA)-cos²A/sinA(sinA-cosA)
=sin³A-cos³A/sinAcosA(sinA-cosA)
=(sinA-cosA)(1+sinAcosA)/sinAcosA(sinA-cosA)
=1+sinAcosA/sinAcosA
=secAcosecA+1
RHS:
1+tanA+cotA
=1+sinA/cosA+cosA/sinA
=sinAcosA+1/sinAcosA
=1+secAcosecA
hence LHS=RHS
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