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 $${\sin ^{50}}x - {\cos ^{50}}x = 1$$