Question

If $\cot \theta =\frac{3}{4}$ , prove that $\sqrt{\frac{\sec \theta -\cos ec\theta }{\sec \theta +\cos ec\theta }}=\frac{1}{\sqrt{7}}$

Answer 1

$cot\theta =\frac{3}{4}\sqrt{\frac{sec\theta -cosec\theta }{sec+cosec\theta }}=\frac{1}{\sqrt{7}}$

$\Rightarrow \frac{sec\theta -cosec\theta }{\sqrt{se{c}^2\theta -cose{c}^2\theta }}=\frac{\frac{5}{3}-\frac{5}{4}}{\sqrt{\frac{25}{9}}-\frac{25}{16}}$

$\Rightarrow \frac{5}{5}\left[\frac{1/12}{\sqrt{7/9\times 16}}\right]=\frac{1}{\sqrt{7}}$