If $3 \sin \theta + 5 \cos \theta = 5$,then the value of $5 \sin \theta - 3 \cos \theta$ will be

If $A + B + C = \pi$ and $\cos A = \cos B \cos C$,then $\tan B \tan C$ is equal to

Number of values of $x \in [0, 2\pi]$ satisfying the equation $\cot x - \cos x = 1 - \cot x \cos x$.

The minimum value of $\sin^{2} \theta + \cos^{2} \theta + \sec^{2} \theta + \operatorname{cosec}^{2} \theta + \tan^{2} \theta + \cot^{2} \theta$ is

If $\operatorname{cosec} \theta - \sin \theta = m$ and $\sec \theta - \cos \theta = n$,then $(m^2 n)^{2/3} + (m n^2)^{2/3} = $

Consider the following two statements.
Statement $p$: The value of $\sin 120^\circ$ can be derived by taking $\theta = 240^\circ$ in the equation $2 \sin \frac{\theta}{2} = \sqrt{1 + \sin \theta} - \sqrt{1 - \sin \theta}$.
Statement $q$: The angles $A, B, C$ and $D$ of any quadrilateral $ABCD$ satisfy the equation $\cos \left( \frac{1}{2}(A + C) \right) + \cos \left( \frac{1}{2}(B + D) \right) = 0$.
Then the truth values of $p$ and $q$ are respectively: