Trigonometric F...

If $$cos\alpha+cos\beta+cos\gamma= 0= sin\alpha+sin\beta+sin\gamma$$ then $$cos2^n\alpha+cos2^n\beta+cos2^n\gamma=?$$

If $$\cos 3x+\sin\left(2x-\dfrac{7\pi}{6}\right)=-2$$, then $$x$$ is equal to $$\left(where\ m\in  Z\right)$$ 

If $${ tan }^{ 2 }\theta +{ cot }^{ 2 }\theta =\frac { a }{ b-cos4\theta  } +c$$ (where defined) is satisfied for all $$\theta $$, then the value of (a + b + c) is equal to $$(a,b,c\in I)$$

If $$sin({ cot }^{ -1 }(x+1)=cos({ tan }^{ -1 }x)$$, then x is equal to 

The value of $$\sin{\left(\alpha+\beta\right)}$$ is 

If $$cos(\alpha +\beta )sin(\gamma +\delta )=cos(\alpha -\beta )sin(\gamma -\delta )$$ then 

In a $$\triangle ABC, \sum a \cos A=4 \sin A \sin B \sin C$$, then value of $$\left(\dfrac{\sum \sin A}{\sum a}\right)^{2}$$ is-

$$sin\left( { 4tan }^{ -1 }{ \cfrac { 1 }{ 3 }  } \right) =$$

If $$0 < \phi < \dfrac {\pi}{2}$$ and if $$\displaystyle x=\sum^{\alpha}_{n=0}\cos^{2}\phi:y=\sum^{\alpha}_{n=0}\sin^{2n}\phi$$ then 

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