Question

Prove: under root (sec theta-1/sec theta+1) + under root (sec theta+1/sec theta-1) = 2 Cosec theta?​

Answer 1

Answer:

Consider LHS

$\sqrt{ \frac{ \sec(θ) - 1 }{ \sec(θ) + 1 } } + \sqrt{ \frac{ \sec(θ) + 1 }{ \sec(θ) - 1 } } \\ \\ = \frac{\sec(θ) - 1 + \sec(θ) + 1}{ \sqrt{(\sec(θ) + 1)(\sec(θ) - 1)} }$

$= \frac{2 \sec(θ) }{ \tan(θ) } \\ \\ = \frac{2 \frac{1}{ \cos(θ) } }{ \frac{ \sin(θ) }{\cos(θ)} }$

$= \frac{2}{ \sin(θ) } \\ \\ = 2 \csc(θ)$

Hence Proved

Hope it helps