Trigonometric F...

if $$\sqrt{2} cos \theta$$ = $$\sqrt { \dfrac { 2+\sqrt { 2+\sqrt { 2 }  }  }{ 2 }  }$$ then the value of $$\theta$$ is 

If $$tan\theta +sin\theta =m$$ and $$tan\theta -sin\theta =n$$ then $$m^2-n^2=$$

The most general solution of $$\tan\theta =-1, \cos\theta =\dfrac { 1 }{ \sqrt { 2 }  } $$ is -

$$cos (4 \pi + \theta)$$ = ...

Consider the operator a = X + $$\dfrac{d}{dx}$$ acting on smooth function of x. The commutator [a, cos x] is

If $${ P }_{ n }=1+{ cos2 }^{ n-1 }\theta -{ sin2 }^{ n-1 }\theta $$ and $${ Q }_{ n }=1+{ tan2 }^{ n-1 }\theta $$ such that $$\overset { r=n }{ \underset { r=1 }{ \Pi  }  } { P }_{ r }{ Q }_{ r-1 }=1$$ (here $$\Pi $$ denotes product of terms) is true for 

The value of $$\dfrac{\sin^{2}2\theta}{\cos^{2}\theta}+\dfrac{\sin^{2}4\theta}{\cos^{2}2\theta}+\dfrac{\sin^{2}\theta}{\cos^{2}4\theta}$$ is $$\left(where \theta=\dfrac{\pi}{7}\right)$$

If $$4\cos{\theta}-3\sec{\theta}=2\tan{\theta}$$, then $${\theta}$$ is equal to

If $$cosx + cos y - cos(x+y) =$$ $$\dfrac{3}{2}$$, then

In $$\Delta ABC, \dfrac{1}{2} a^2 \dfrac{sin B \, sin C}{sin A} = $$