Question : If $\tan 2 \theta=\cot \left(\theta-36^{\circ}\right)$, where $2 \theta$ is an acute angle, then the value of $\theta$ is:

Option 1: 18°

Option 2: 36°

Option 3: 30°

Option 4: 42°

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 $\tan \theta-\cot \theta=4$, then find the value of $\tan ^2 \theta+\cot ^2 \theta$.

Option 1: 16

Option 2: 20

Option 3: 14

Option 4: 18

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

Option 1: $-1$

Option 2: $1$

Option 3: $-\sqrt{3}$

Option 4: $\sqrt{3}$