यदि $5 \sin ^{2} \theta+3 \cos ^{2} \theta=4$, $\tan \theta$ का मूल्य है

$5 \sin ^{2} \theta+3 \cos ^{2} \theta=4$

$\Rightarrow 5 \frac{\sin ^{2} \theta}{\cos ^{2} \theta}+3 \frac{\cos ^{2} \theta}{\cos ^{2} \theta}=\frac{4}{\cos ^{2} \theta}$

$\Rightarrow 5 \tan ^{2} \theta+3=4 \sec ^{2} \theta$

$\Rightarrow 5 \tan ^{2} \theta+3=4\left(1+\tan ^{2} \theta\right)$

$\Rightarrow 5 \tan ^{2} \theta+3=4+4 \tan ^{2} \theta$

$\Rightarrow 5 \tan ^{2} \theta-4 \tan ^{2} \theta=4-3$

$\Rightarrow \tan ^{2} \theta=1$

$\Rightarrow \tan \theta=\pm 1$