Trigonometric F...

If $\sin { x } +\cos { x } =a,$ then $\left| \sin { x } -\cos { x }  \right|$ equals

The number of solution of the equation $\sin 5x \cos 3x=\sin 6x \cos 2x$ in the interval $[0,\pi]$ is

The value of $\theta$ satisfying $\sin{7\theta}=\sin{4\theta}-\sin{\theta}$ and $\theta<0<\pi/2$ are-

Evaluate $\tan \left[ {\dfrac{\pi }{4}\, + \,\dfrac{1}{2}\,{{\cos }^{ - 1}}\,\dfrac{a}{b}} \right]\, + \,\tan \left[ {\dfrac{\pi }{4}\, - \,\dfrac{1}{2}{{\cos }^{ - 1}}\,\dfrac{a}{b}} \right]\, =$

If $A+B+C=\pi$ then $\sin^3A \cos(B-C)+ \sin^3\cos(C-A) + \sin^3C \cos (A-B)$ is equal to

If $(\cos\theta +\cos 2\theta)^3=\cos^3\theta +\cos^32\theta$, then the least positive value of $\theta$ is equal to?

General solution of equation $\cot \theta  + \text{cosec}\theta  = \sqrt 3$ is

If $sin 2 \theta = cos 3 \theta \, and \, \theta$ is acute then $sin 5 \theta$  = ...

The general solution of the equation ${\sin ^{50}}x - {\cos ^{50}}x = 1$