Prove that ,Sin A(1+tanA)+cosA(1+cotA)=(secA+cosecA)

1.	Prove that ,Sin A(1+tanA)+cosA(1+cotA)=(secA+cosecA)
Answer» sinA(1+tanA)+cosA(1+cotA)=secA+cosecA.....solving LHS first....sinA(1+sinA/cosA)+cosA(1+cosA/sinA) [since we know that tanA =sinA/cos/A and cotA=cosA/sinA]=sinA(cosA+sinA/cosA)+cosA(sinA+cosA/sinA)=sinA+cosA{sinA/cosA+cosA/sinA}.....[taking sinA+cosA as common]=sinA+cosA(1-cos^2A+cos^2A)/sinA•cosA=(sinA+cosA)/(sinA•cosA)........now solving RHS.....secA+cosecA=1/cosA+1/sinA=(sinA+cosA)/(sinA•cosA).... Since LHS=RHS....Hence proved..??

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