Question

Prove that

$\frac{\cos ecA+1}{\cos ecA-1}=\frac{1+\sin A}{1-\sin A}$

Answer 1

Prove that:-$\frac{\csc A+1}{\csc A-1}=\frac{1+\sin A}{1-\sin A}$

$LHS=\frac{\csc A+1}{\csc A-1}=\frac{\frac{1}{\sin A}+1}{\frac{1}{\sin A}-1}=\frac{\frac{1+\sin A}{\sin A}}{\frac{1-\sin A}{\sin A}}=\frac{1+\sin A}{1-\sin A}=RHS$