If tan θ = 1/√7, show that cosec^2 θ - sec^2 θ/cosec^2 θ + sec^2 θ = 3/4

Question

If tan θ = \(\frac{1}{\sqrt{7}}\), show that \(\frac{cosec^2θ-sec^2θ}{cosec^2θ+sec^2θ}\) = \(\frac{3}{4}\)

Answer 1

\(\frac{cosec^2θ-sec^2θ}{cosec^2θ+sec^2θ}\)

Hence Proved.