Question : Find the value of the following expression.
$5\left(\sin ^4 \theta+\cos ^4 \theta\right)+3\left(\sin ^6 \theta+\cos ^6 \theta\right)+19 \sin ^2 \theta \cos ^2 \theta$

Question : Simplify the following expression.
$\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$

Question : The expression $\frac{\left(1-2 \sin ^2 \theta \cos ^2 \theta\right)(\cot \theta+1) \cos \theta}{\left(\sin ^4 \theta+\cos ^4 \theta\right)(1+\tan \theta) \operatorname{cosec} \theta}-1,0^{\circ}<\theta<90^{\circ}$, equals:

Question : If $\sin\theta+\sin^{2}\theta=1$, then the value of $\cos^{12}\theta+3\cos^{10}\theta+3\cos^{8}\theta+\cos^{6}\theta-1$ is:

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