Question : If $\frac{\sec \theta+\tan \theta}{\sec \theta–\tan \theta}=2 \frac{51}{79}$, then the value of $\sin \theta$ is equal to:

Option 1: $\frac{35}{72}$

Option 2: $\frac{39}{72}$

Option 3: $\frac{91}{144}$

Option 4: $\frac{65}{144}$

Question : Which of the following is equal to $[\frac{\tan \theta+\sec \theta–1}{\tan \theta–\sec \theta+1}]$?

Option 1: $\frac{1+\sin \theta}{\cos \theta}$

Option 2: $\frac{1+\tan \theta}{\cot \theta}$

Option 3: $\frac{1+\cot \theta}{\tan \theta}$

Option 4: $\frac{1+\cos \theta}{\sin \theta}$

Question : Find the value of: $\sqrt{\frac{1 - \sin 3 \theta}{1 + \sin 3 \theta}}$

Option 1: $\sec 3 \theta - \tan 3 \theta$

Option 2: $(\sec 3 \theta - \tan 3 \theta)^3$

Option 3: $(\sec 3 \theta - \tan 3 \theta)^2$

Option 4: $\sec 3 \theta + \tan 3 \theta$

Question : If $\tan \theta=\frac{4}{3}$, then the value of $\frac{3\sin \theta+ 2\cos \theta}{3\sin \theta – 2 \cos \theta}$ is:

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

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

Option 3: $3$

Option 4: $–3$

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 : If $\sec\theta-\tan\theta=\frac{1}{\sqrt3}$, then the value of $\sec\theta.\tan\theta$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{2}{\sqrt3}$

Option 3: $\frac{4}{\sqrt3}$

Option 4: $\frac{1}{\sqrt3}$