What is the value of $\frac{[\sin (y-z)+\sin (y+z)+2 \sin y]}{[\sin (x-z)+\sin (x+z)+2 \sin x]} = ?$

The minimum value of $3 \cos x + 4 \sin x + 5$ is

The value of $\frac{\sin 300^{\circ} \tan 240^{\circ} \sec \left(-420^{\circ}\right)}{\cot \left(-315^{\circ}\right) \cos \left(210^{\circ}\right) \operatorname{cosec}\left(-315^{\circ}\right)}$ is

The value of $\sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + \dots + \sin^2 85^\circ + \sin^2 90^\circ$ is equal to

In a right-angled triangle,the hypotenuse is $2 \sqrt{2}$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are

If $\sin 6\theta = 32\cos^5 \theta \sin \theta - 32\cos^3 \theta \sin \theta + 3x,$ then $x = $