R D Sharma Solutions for Chapter: Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Exercise 1: EXERCISE 9.1

If $\sin \alpha +\sin \beta =a$ and $\cos \alpha +\cos \beta =b$, then prove that $\cos (\alpha -\beta )=\frac{a^2+b^2-2}{2}$.

The value of $\cos \left(36°-A\right)\cos \left(36°+A\right)+\cos \left(54°-A\right)\cos \left(54°+A\right)$ is

The value of $\tan x \tan \left(\frac{\pi }{3}-x\right)\tan \left(\frac{\pi }{3}+x\right)$ is

The value of $\tan x+\tan \left(\frac{\pi }{3}+x\right)+\tan \left(\frac{2\pi }{3}+x\right)$ is

The value of $\frac{\sin 5\alpha -\sin 3\alpha }{\cos 5\alpha +2\cos 4\alpha +\cos 3\alpha }$ is

If $x=0°$, then $\frac{\sin 5x}{\sin x}$ is equal to

If $a\cos 2x+b\sin 2x=c$ has $\alpha$ and $\beta$ as its roots, then prove that $\tan \alpha \tan \beta =\frac{c-a}{c+a}$.

If $n=1, 2, 3,\dots$, then $\cos \alpha \cos 2\alpha \cos 4\alpha \dots \cos 2^{n-1}\alpha$ is equal to