Question

Prove that $\sqrt{\frac{\sec \theta +1}{\sec \theta -1}}=\cot \theta +cosec\theta$

Answer 1

$\sqrt{\frac{\sec \theta +1}{\sec \theta -1}}=\cot \theta +\csc \theta LHS=\sqrt{\frac{\frac{1}{\cos \theta }+1}{\frac{1}{\cos \theta }-1}}=\sqrt{\frac{\frac{1}{\cos \theta }+1}{\frac{1}{\cos \theta }-1}\times \frac{\frac{1}{\cos \theta }+1}{\frac{1}{\cos \theta }+1}}=\sqrt{\frac{1+\cos \theta }{\sin \theta }}=\csc \theta +\cot \theta$