Question

(1+tanA/sinA)+(1+cotA/cosA)=2(secA+cosecA)
please reply fast it's urgent​

Answer 1

(1+TanA/SinA) + (1+CotA/CosA) = (1+1/CosA) + (1+1/SinA) = 2+SecA+CosecA
So 2 + SecA + CosecA = 2SecA + 2CosecA (given)
SecA + CosecA = 2
(SinA + CosA)/(SinA*CosA) = 2
SinA + CosA = 2SinACosA

Squaring both sides,
1 + 2SinACosA = 4(SinACosA)^2
1 + Sin2A = (Sin2A)^2

Let Sin2A = t
So, 1+t=t^2
t = (1 + sqrt(5))/2 or (1 - sqrt(5))/2 {sqrt = square root}
So Sin 2A = (1 + sqrt(5))/2 or (1 - sqrt(5))/2

Hope it helps