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

Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:

Question : If $\frac{(3 \sin \theta-\cos \theta)}{(\cos \theta+\sin \theta)}=1$, then the value of $\cot \theta$ is:

Question : If $\sin \theta-\cos \theta=0$, then find the value of $\left(\sin^3 \theta-\cos^3 \theta\right)$.

Question : If $x\sin^{3}\theta +y\cos^{3}\theta=\sin\theta\cos\theta$ and $x\sin\theta-y\cos\theta=0$, then the value of $\left ( x^{2}+y^{2} \right )$ equals: