Question

Prove that 1+cosA/sinA + sinA/1+cosA=2cosecA

Answer 1

`(1+cos\alpha)/(sin\alpha)+(sin\alpha)/(1+cos\alpha)=2cosec\alpha\\\\L=((1+cos\alpha)(1+cos\alpha)+sin\alpha\cdot sin\alpha)/(sin\alpha(1+cos\alpha))=(1+2cos\alpha+cos^2\alpha+sin^2\alpha)/(sin\alpha(1+cos\alpha))\\\\=(1+2cos\alpha+1)/(sin\alpha(1+cos\alpha))=(2+2cos\alpha)/(sin\alpha(1+cos\alpha))=(2(1+cos\alpha))/(sin\alpha(1+cos\alpha))\\\\=(2)/(sin\alpha)=2\cdot(1)/(sin\alpha)=2cosec\alpha=R`