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:

Question : If $\sin \theta-\cos \theta=\frac{4}{5}$, then find the value of $\sin \theta+\cos \theta$.

Question : If $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$

Question : If $\cos \theta+\cos ^2 \theta=1$, find the value of $\sqrt{\sin ^4 \theta+\cos ^2 \theta}$.

Question : $\cos \left(30^{\circ}+\theta\right)-\sin \left(60^{\circ}-\theta\right)=$ _____________.