If $\tan \theta + \cot \theta = 5,$ then $\tan^2 \theta + \cot^2 \theta$ is

If $\cos ^{2} x+\cos ^{4} x=1,$ then $\tan ^{2} x+\tan ^{4} x=?$

The value of $\frac{\tan 70^\circ - \tan 20^\circ}{\tan 50^\circ} = $

The value of $(\sec \theta + \operatorname{cosec} \theta)$ when $\theta = 45^{\circ}$ is: (in $\sqrt{2}$)

The numerical value of $\frac{\cos ^{2} 45^{\circ}}{\sin ^{2} 60^{\circ}}+\frac{\cos ^{2} 60^{\circ}}{\sin ^{2} 45^{\circ}}-\frac{\tan ^{2} 30^{\circ}}{\cot ^{2} 45^{\circ}}-\frac{\sin ^{2} 30^{\circ}}{\cot ^{2} 30^{\circ}}$ is

If $\tan \theta = \frac{1}{\sqrt{11}}$ and $0 < \theta < \frac{\pi}{2},$ then the value of $\frac{\operatorname{cosec}^{2} \theta - \sec ^{2} \theta}{\operatorname{cosec}^{2} \theta + \sec ^{2} \theta}$ is