Question

f
A+B=90
prove that
(sinA + SinB)² = 1 + 2 sinA. COSA​

Answer 1

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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