Question

anybody who can solve this question​

Answer 1

Question :-

solve it :

$\to \frac{ { \cos}^{2} \theta }{ { \cot}^{2} \theta - { \cos}^{2} \theta } = 3$

Answer :-

$\boxed{ \theta = \frac{ \pi}{3} \: or \: 60 \degree} \:$

Explanation :-

we have ,

$\to \frac{ { \cos}^{2} \theta }{ { \cot}^{2} \theta - { \cos}^{2} \theta } = 3 \\ \\ \to \: { \cos}^{2} \theta = 3 { \cot}^{2} \theta - 3 { \cos}^{2} \theta \\ \\ \to \: { \cos}^{2} \theta + 3 { \cos}^{2} \theta = 3 { \cot}^{2} \theta \\ \because \cot \theta = \frac{ \cos \theta}{ \sin \theta} \\ \\ \to \: 4 { \cos}^{2} \theta =3 \frac{ { \cos}^{2} \theta }{ { \sin}^{2} \theta} \\ \\ \to \: 4 { \sin}^{2} \theta = 3 \\ \\ \to \: { \sin}^{2} \theta = \frac{3}{4} \\ \\ \bf taking \: \sqrt{} \: on \: both \: sides \\ \\ \to \sqrt{ { \sin}^{2} \theta } = \sqrt{ \frac{3}{4} } \\ \\ \to \: \sin \theta = \frac{ \sqrt{3} }{2} \: \: \because \: \sin \: \frac{ \pi}{3} = \frac{ \sqrt{3} }{2} \\ \\ \to \: \sin \theta = \sin \frac{ \pi}{3} \\ \\ \to \boxed{ \theta = \frac{ \pi}{3} \: or \: 60 \degree}$

Hope it will helps you.