Prove that $$ \frac{1}{\sec heta-1}+\frac{1}{\sec heta+1}=\left[2 \cos heta \operatorname{cosec}^{2} heta ight] $$

Question

Prove that $$ \frac{1}{\sec 	heta-1}+\frac{1}{\sec 	heta+1}=\left[2 \cos 	heta \operatorname{cosec}^{2} 	hetaight] $$

Peters Carter · Accepted Answer

The identity is proven: $$ \frac{1}{\sec 	heta - 1} + \frac{1}{\sec 	heta + 1} = 2 \cos 	heta \csc^2 	heta $$.

Prove that \( \frac{1}{\sec \theta-1}+\frac{1}{\sec \theta+1}=\left[2 \cos \theta \operatorname{cosec}^{2} \theta\right] \)