Question : Find the value of $\tan (50°+\theta)-\operatorname{cot}(40°-\theta)$.

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

Option 2: $-1$

Option 3: $0$

Option 4: $1$

Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

Option 3: $2 \cot \theta$

Option 4: $\operatorname{cosec} \theta+\cot \theta$

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 $\operatorname{cos} \theta=\frac{4}{5}$, find the value of $\operatorname{cot} \theta+\tan \theta$.

Option 1: $\frac{12}{25}$

Option 2: $\frac{25}{12}$

Option 3: $\frac{27}{12}$

Option 4: $\frac{12}{27}$

Question : If $\operatorname{tan} \theta=\frac{3}{4}$, then find the value of expression $\frac{1+\operatorname{sin} \theta}{1-\operatorname{sin} \theta}$.

Option 1: 4

Option 2: 3

Option 3: 8

Option 4: 5

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