If $0 \leq x \leq \frac{\pi}{2}$, then the number of values of $x$ for which $\sin x - \sin 2x + \sin 3x = 0$ is

Let $f(x) = \frac{\sin(x-a) + \sin(x+a)}{\cos(x-a) - \cos(x+a)}$,then

$\cos^2 76^{\circ} + \cos^2 16^{\circ} - \cos 76^{\circ} \cos 16^{\circ}$ is equal to

Let $\alpha$ and $\beta$ be nonzero real numbers such that $2(\cos \beta - \cos \alpha) + \cos \alpha \cos \beta = 1$. Then which of the following is/are true?

Let $\alpha, \beta$ be two real numbers such that $\pi < (\alpha-\beta) < 3 \pi$. If $\sin \alpha+\sin \beta=\frac{-21}{65}$ and $\cos \alpha+\cos \beta=\frac{-27}{65}$,then $\cos \left(\frac{\beta-\alpha}{2}\right)=$

If $\cot \theta + \tan \theta = 3$ and $1 - \cos^2 \theta - \alpha \cos \theta = 0$,then