Question

The value of $\frac{\text{cosec}A}{\text{cosec}A-1}+\frac{\text{cosec}A}{\text{cosec}A+1}=m{\sec }^{2}A$. Then $m$ is:

Answer 1

Given:$\frac{\frac{1}{sinA}}{\frac{1}{sinA}-1}+\frac{\frac{1}{sinA}}{\frac{1}{sinA}+1}\Rightarrow \frac{1}{1-sinA}+\frac{1}{1+sinA}\Rightarrow \frac{1-sinA+1-sinA}{(1-sinA)(1+sinA)}\Rightarrow \frac{2}{1-{sin}^{2}A}\because [{sin}^2\theta +{cos}^2\theta =1][sec\theta =\frac{1}{cos\theta }]\Rightarrow 2{sec}^{2}A=RHSSo,m=2$