Question

2cos^2theta=1/2 , find cosec^2theta + cot^theta​

Answer 1

$2 {cos}^{2} \theta = \frac{1}{2} \\ {cos}^{2} \theta = \frac{1}{4} \\ cos \theta = \frac{1}{2} \\ \theta = 60 \degree \\ now \: \: \: \: {cosec}^{2} \theta + {cot}^{2} \theta \\ = {cosec}^{2} 60 + {cot}^{2} 60 \\ = ( { \frac{2}{ \sqrt{3} } })^{2} + ( { \frac{1}{ \sqrt{3} } })^{2} \\ = \frac{4}{3} + \frac{1}{3} \\ = \frac{5}{3}$