Question : The value of $\tan θ + \cot θ − \sec θ \operatorname{cosec} θ$ is:

Option 1: $2$

Option 2: $−2$

Option 3: $0$

Option 4: $\frac{1}{2}$

Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:

Option 1: $\sec\theta+\tan \theta$

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

Option 3: $\operatorname{cosec} \theta+\cot \theta$

Option 4: $\sec\theta-\tan \theta$

Question : $\frac{(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)}{(\sec \theta+\tan \theta)(1-\sin \theta)}$ is equal to:

Option 1: $2 \sec \theta$

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

Option 3: $\operatorname{cosec} \theta$

Option 4: $\sec \theta$

Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\operatorname{cosec} \theta \sec \theta$

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

Option 3: $\sin \theta \cos \theta$

Option 4: $\sec \theta$

Question : For any real values of $\theta, \sqrt{\frac{\sec\theta \:-\: 1}{\sec\theta \:+\: 1}}=$?

Option 1: $\cot\theta - \operatorname{cosec}\theta$

Option 2: $\sec\theta - \tan\theta$

Option 3: $\operatorname{cosec}\theta - \cot\theta$

Option 4: $\tan\theta - \sec\theta$

Question : If $\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta}=\frac{1}{7}, \theta$ lies in first quadrant, then the value of $\frac{\operatorname{cosec} \theta+\cot ^2 \theta}{\operatorname{cosec} \theta-\cot ^2 \theta}$ is:

Option 1: $\frac{19}{5}$

Option 2: $\frac{22}{3}$

Option 3: $\frac{37}{12}$

Option 4: $\frac{37}{19}$