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 : The value of $\frac{\sin\theta-2\sin^{3}\theta}{2\cos^{3}\theta-\cos\theta}$ is equal to:

Option 1: $\sin\theta$

Option 2: $\cos\theta$

Option 3: $\tan\theta$

Option 4: $\cot\theta$

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 $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, 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 $\sin \theta-\cos \theta=0$, then what is the value of $\sin ^2 \theta+\tan ^2 \theta$ ?

Option 1: $\frac{1}{2}$

Option 2: $1$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{2}$