If $2 \cos \theta + \sin \theta = 1$ $\left( \theta \neq \frac{\pi}{2} \right)$,then $7 \cos \theta + 6 \sin \theta$ is equal to

If $2y \cos \theta = x \sin \theta$ and $2x \sec \theta - y \csc \theta = 3$,then $x^2 + 4y^2 = $

Assertion $(A)$: If $\sqrt{4 \sin^4 \theta + \sin^2 2\theta} + 4 \cos^2\left(\frac{\pi}{4} - \frac{\theta}{2}\right) = 2$,then $\theta$ lies in the $3^{\text{rd}}$ quadrant or $4^{\text{th}}$ quadrant.
Reason $(R)$: $\sqrt{\sin^2 \theta} = \sin \theta$

Let $\frac{\pi}{2} < \theta < \pi$ and $\cot \theta = -\frac{1}{2 \sqrt{2}}$. Then the value of $\sin (\frac{15 \theta}{2}) (\cos 8 \theta + \sin 8 \theta) + \cos (\frac{15 \theta}{2}) (\cos 8 \theta - \sin 8 \theta)$ is equal to:

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $A_0 A_1$,$A_0 A_2$,and $A_0 A_4$ is

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to