Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:

Question : If $\operatorname{cosec} \theta-\cot \theta=\frac{7}{2}$, then the value of $\operatorname{cosec} \theta$ will be:

Question : If $\sin \theta+\cos \theta=\frac{1}{29}$, then find the value of $\frac{\operatorname{sin} \theta+\operatorname{cos} \theta}{\operatorname{sin} \theta-\operatorname{cos} \theta}$.

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

Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is: