Question

someone, solve this. ​

Answer 1

$\tan\theta = \frac{1}{ \sqrt{3} }$

$\implies \tan\theta = \tan30 \degree$

$\therefore \theta = 30 \degree$

$\frac{\cosec^2\theta-\sec^2\theta}{\cosec^2\theta+\sec^2\theta}$

$\implies\frac{\cosec^2 30\degree-\sec^230\degree}{\cosec^230\degree+\sec^230\degree}$

$\implies\frac{ {2}^{2} - { (\frac{2}{ \sqrt{3} } )}^{2} }{{2}^{2} + { (\frac{2}{ \sqrt{3} } )}^{2}}$

$\implies\frac{ 4 - \frac{4}{3} }{4 + \frac{4}{3}}$

$\implies\frac{ \frac{12 - 4}{3} }{ \frac{12 + 4}{3}}$

$\implies\frac{ 8 }{ 16}$

$\orange{ \therefore\frac{ 1 }{ 2}}$

HOPE IT HELPS!!