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 : 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 : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, 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 : Find the value of $\tan 3 \theta$, if $\sec 3 \theta=\operatorname{cosec}\left (4 \theta-15°\right)$.

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

Option 2: $\sqrt3$

Option 3: $–1$

Option 4: $1$

Question : $\theta$ is a positive acute angle and $\sin\theta-\cos\theta=0$, then the value of $\sec\theta+\operatorname{cosec}\theta$ is:

Option 1: $2$

Option 2: $\sqrt{3}$

Option 3: $2\sqrt{2}$

Option 4: $3\sqrt{2}$