sin θ = \(\frac{3}4\)
⇒ cosθ = \(\frac{\sqrt{7}}4\)
\(\sqrt{\frac{cosec^2θ -cot^2θ}{sec^2θ-1}}\)
= \(\sqrt{\frac{1+cot^2θ -cot^2θ}{1+tan^2θ-1}}\)
= \(\sqrt{\frac{1}{tan^2\theta}}\)
= cotθ = \(\frac{cosθ}{sinθ}\)
= \(\frac{\sqrt{7}}4\) = \(\frac{4}3\) = \(\frac{\sqrt{7}}3\)