The expression $\cos^2(A - B) + \cos^2 B - 2\cos(A - B)\cos A\cos B$ is

If $\cos \theta = \frac{3}{5}$ and $\cos \phi = \frac{4}{5},$ where $\theta$ and $\phi$ are positive acute angles,then $\cos \frac{\theta - \phi}{2} = $

If $\tan \theta - \cot \theta = 0$ and $\theta$ is a positive acute angle,then the value of $\frac{\tan (\theta + 15^{\circ})}{\tan (\theta - 15^{\circ})}$ is

If $\tan \theta = \sqrt{\frac{3}{2}}$,the sum of the infinite series $1 + 2(1 - \cos \theta) + 3(1 - \cos \theta)^2 + 4(1 - \cos \theta)^3 + \dots \infty$ is

If $\sin \theta + \cos \theta = \sqrt{2} \cos \theta$,then the value of $(\cos \theta - \sin \theta)$ is

For any $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$,the expression $3(\sin \theta - \cos \theta)^4 + 6(\sin \theta + \cos \theta)^2 + 4\sin^6 \theta$ equals