Question

$\csc \theta =\sqrt{2}them\frac{2{\sin }^2\theta +3{\cot }^2\theta }{4{\tan }^2\theta -{\cos }^2\theta }=$?

Answer 1

$\text{cosec}\theta =\sqrt{2}⟹\theta =\frac{\pi }{4}$

$\frac{2{\sin }^2\theta +3{\cot }^2\theta }{4{\tan }^2\theta -{\cos }^2\theta }=\frac{2(\frac{1}{2})+3\left(1\right)}{4(1{)}^2-\frac{1}{2}}=\frac{4}{4-\frac{1}{2}}=\frac{8}{7}$