Question

$\frac{\text{cosec}A}{\text{cosec}A-1}+\frac{\text{cosec}A}{\text{cosec}A+1}=m{\sec }^{2}A$. Find $m$.

Answer 1

Since, $\frac{cosecA}{cosecA-1}+\frac{cosecA}{cosecA+1}=m{\sec }^{2}A$

$⟹\frac{{cosec}^{2}A+cosecA+co{sec}^{2}A-cosecA}{{cosec}^{2}A-1}=m{\sec }^{2}A$

$⟹\frac{2cose{c}^{2}A}{{\cos }^{2}A}=m{\sec }^{2}A$

$⟹\frac{2}{{\sin }^{2}A}\times \frac{{\sin }^{2}A}{{\cos }^{2}A}=m{\sec }^{2}A$

$⟹2{\sec }^{2}A=m{\sec }^{2}A$

$⟹2=m$