The value of $( an A \operatorname{cosec} A)^{2}-(\sin A \sec A)^{2}$ is :\

Question

The value of $(	an A \operatorname{cosec} A)^{2}-(\sin A \sec A)^{2}$ is :\

Professor PC Thomas Classes · Answer

(b) : We have,\ $(	an A \cdot \operatorname{cosec} A)^{2}-(\sin A \cdot \sec A)^{2}$\ $\Rightarrow\left(\frac{\sin A}{\cos A} 	imes \frac{1}{\sin A}ight)^{2}-\left(\frac{\sin A}{\cos A}ight)^{2}$\ $=\frac{1}{\cos ^{2} A}-\frac{\sin ^{2} A}{\cos ^{2} A}=\frac{1-\sin ^{2} A}{\cos ^{2} A}=\frac{\cos ^{2} A}{\cos ^{2} A}=1$