prove (sin a ÷1+cos) +(1+cos a÷sin a)=2 cosec a

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Solution

Given {sinA/1+cosA }+{1+CosA /sinA}=2cosecA
Take LHS
={SinA/1+cosA}+{1+cosA/sinA}
solve….this
It becomes
=SinA. SinA+(1+cosA)(1+cosA)/sinA(1+cosA)
=sin^2A+(1+cosA)^2 / sinA(1+cosA)
=sin^2A+cos^2A+1+2cosA /sinA(1+cosA)
we know identity ,
Sin^2A+Cos^2A=1
It becomes,
=1+1+2cosA/sinA(1+CosA)
=2(1+cosA)/sinA(1+cosA)
=2/sinA
= 2CosecA
Hence proved..

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