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

If $\sec A = a + \left(\frac{1}{4a}\right)$,then $\sec A + \tan A =$

If $\cos(\alpha + \beta) = \frac{3}{5}$,$\sin(\alpha - \beta) = \frac{5}{13}$ and $0 < \alpha, \beta < \frac{\pi}{4}$,then $\tan(2\alpha)$ is equal to

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

If $2 \sin \theta + \cos \theta = \frac{7}{3},$ then the value of $(\tan^2 \theta - \sec^2 \theta)$ is

If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is