Question : If $\theta$ be an acute angle and $\tan \theta+\cot \theta=2$, then the value of $2 \tan ^2 \theta+\cot ^2 \theta+\tan ^4 \theta \cot ^4 \theta$ is:

Question : If $\tan(5\theta-10^\circ)=\cot(5\varphi+20^\circ)$, then the value of $(\theta+\varphi)$ is:

Question : If $\tan \theta+\sin \theta=A$ and $\tan \theta-\sin \theta=B$, then what is the value of $A^2-B^2$?

Question : If $\tan \theta \cdot \tan 2 \theta=1$, then the value of $\cot 5 \theta$ is:

Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?