Question : The value of $\frac{\sin\theta-2\sin^{3}\theta}{2\cos^{3}\theta-\cos\theta}$ is equal to:

Option 1: $\sin\theta$

Option 2: $\cos\theta$

Option 3: $\tan\theta$

Option 4: $\cot\theta$

Question : If $5\tan\theta=4$, then $\frac{5\sin\theta-3\cos\theta}{5\sin\theta+2\cos\theta}$ is equal to:

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

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

Option 3: $\frac{1}{6}$

Option 4: $\frac{1}{3}$

Question : If $\sin \theta-\cos \theta=0$, then what is the value of $\sin ^2 \theta+\tan ^2 \theta$ ?

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

Option 2: $1$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{2}$

Question : What is the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$?

Option 1: $\frac{1}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 2: $2\left(\sin ^2 \theta-\cos ^2 \theta\right)$

Option 3: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Option 4: $\sin ^2 \theta-\cos ^2 \theta$

Question : If $3 \tan \theta=2$, what is the value of $\frac{(3 \sin \theta-\cos \theta)}{(3 \sin \theta+\cos \theta)}?$

Option 1: $1$

Option 2: $3$

Option 3: $\sqrt3$

Option 4: $\frac{1}{3}$