Trigonometric F...

The principal value of 
     $$ cos^{-1} \left (cos\dfrac{2\pi}{3} \right ) + sin^{-1} \left (sin\dfrac{2\pi}{3} \right ) $$ is

Evaluate : $$ tan \left [ 2\, tan^{-1}\dfrac{1}{5} - \dfrac{\pi}{4} \right ] $$

The value of $$ \dfrac{3 \pi}{4} $$ in sexagesimal system is:

The value of $$ \dfrac{5}{16} $$ right angles in sexagesimal system is equal to 

1 radian is equal to:

How many right angles is equal to $$56^{\circ} 15' $$ ?

The positive integer value of $$n >3$$ satisfying the equation
$$ \displaystyle{\dfrac{1}{\sin \left(\dfrac{\pi}{n}\right)}=\dfrac{1}{\sin\left(\dfrac{2\pi}{n}\right)}+\dfrac{1}{\sin\left(\dfrac{3\pi}{n}\right)}
}$$ is

The solution set of the equation

The general solution of $$\sin x  - 3\sin 2x + \sin 3x
= \cos x - 3\cos 2x + \cos 3x$$ is

Assertion :  lf $$x = \sin (\alpha-\beta)\sin (\gamma-\delta)$$ ,$$y = \sin (\beta-\gamma) \sin (\alpha-\delta)$$, $$z = \sin (\gamma-\alpha) \sin (\beta-\delta)$$,  then $$x+y+z = 0$$
Reason : $$2 \sin {A}\sin {B} = \cos {(A-B)}+\cos {(A+B)}$$