Question : The minimum value of $4\tan^{2}\theta+9\cot^{2}\theta$ is equal to:

Option 1: 0

Option 2: 5

Option 3: 12

Option 4: 13

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:

Option 1: 4

Option 2: 2

Option 3: 3

Option 4: 6

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

Option 1: $\frac{4}{3}$

Option 2: $\frac{10}{3}$

Option 3: $3$

Option 4: $\frac{6}{5}$

Question : If $0^{\circ}< \theta< 90^{\circ}$ and $\operatorname{cosec \theta} =\cot^{2}\theta$, then the value of expression $\operatorname{cosec^{4}\theta}–\operatorname{2cosec^{2}\theta}-\cot^{2}\theta$ is equal to:

Option 1: $2$

Option 2: $0$

Option 3: $1$

Option 4: $3$

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

Option 1: $\tan \theta \sin \theta$

Option 2: $4 \cot \theta$

Option 3: $4 \tan \theta \sin \theta$

Option 4: $2 \tan \theta \sin \theta$

Question : If $\tan \theta -\cot \theta =0$, find the value of $\sin \theta +\cos \theta$.

Option 1: $0$

Option 2: $1$

Option 3: $\sqrt{2}$

Option 4: $2$