The value of $\cos 15^\circ - \sin 15^\circ$ is equal to

If $\sec \theta - \tan \theta = \frac{a+1}{a-1},$ then $\cos \theta =$

$\frac{\sin^3 \theta - \cos^3 \theta}{\sin \theta - \cos \theta} - \frac{\cos \theta}{\sqrt{1 + \cot^2 \theta}} - 2 \tan \theta \cot \theta = -1$ if

Maximum value of $5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) - 1$ is

The value of $\sin 105^{\circ} + \cos 105^{\circ}$ is

If $\tan \alpha$ equals the integral solution of the inequality $4x^2 - 16x + 15 < 0$ and $\cos \beta$ equals the slope of the bisector of the first quadrant,then $\sin(\alpha + \beta)\sin(\alpha - \beta)$ is equal to