If cotθ = 3/4, prove that √secθ - cosecθ/secθ + cosecθ = 1/ √7

Question

If cotθ = \(\frac{3}4\), prove that \(\sqrt{\frac{secθ-cosecθ}{secθ+cosecθ}}\) = \(\frac{1}{\sqrt{7}}\)

Answer 1

cotθ = \(\frac{3}4\)

⇒ sinθ = \(\frac{4}5\)

or cosecθ = \(\frac{5}4\)

and cosθ = \(\frac{3}5\)

or secθ = \(\frac{5}3\)