SOLUTION: Please help to Prove that (cot^2A+sec^2A)/(tan^2A+cosec^2A) = sinAcosA(tanA+cotA)

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Question 969980: Please help to Prove that (cot^2A+sec^2A)/(tan^2A+cosec^2A) = sinAcosA(tanA+cotA)
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
LHS.
=%28cot%5E2%28A%29%2Bsec%5E2%28A%29%29%2F%28tan%5E2%28A%29%2Bcosec%5E2%28A%29%29
.
=
.
=%28cos%5E4%28A%29%2Bsin%5E2%28A%29%29%2F%28sin%5E4%28A%29%2Bcos%5E2%28A%29%29
.
=%28%281-sin%5E2%28A%29%29%5E2%2Bsin%5E2%28A%29%29%2F%28sin%5E4%28A%29%2Bcos%5E2%28A%29%29
.
=%281%2Bsin%5E4%28A%29-sin%5E2%28A%29%29%2F%28sin%5E4%28A%29%2Bcos%5E2%28A%29%29
.
=%28sin%5E4%28A%29%2Bcos%5E2%28A%29%29%2F%28sin%5E4%28A%29%2Bcos%5E2%28A%29%29
.
=1
.
=sin%5E2%28A%29%2Bcos%5E2%28A%29
.
=sin%28A%29cos%28A%29%2A%28sin%28A%29%2Fcos%28A%29%2Bcos%28A%29%2Fsin%28A%29%29(Taking out sinAcosA as common)
.
=sin%28A%29cos%28A%29%2A%28tan%28A%29%2Bcot%28A%29%29
= RHS.