Trigonometric F...

The number of solution of $$\sec x \cos 5x+1=0$$ in the interval $$[0,2\pi]$$ is

If $$2 \tan ^ { 2 } \theta - 5 \sec \theta = 1$$ has exactly $$7$$ solutions in the interval $$\left[ 0 , \dfrac { n \pi } { 2 } \right] , n \in N$$ then the least and  greatest values of $$n$$ are 

The value of $$\sqrt { 3 } \cot 20 ^ { \circ } - 4 \cos 20 ^ { \circ }$$ = __________________________.

If in a triangle $$ABC, \dfrac{b+c}{11}=\dfrac{c+a}{12}=\dfrac{a+b}{13}$$, then $$\cos A$$ is equal to:

The number of real solutions of the equation $$\sin \left( e ^ { x } \right) = 5 ^ { x } + 5 ^ { - x }$$ is ____________________.

The value of $$\sin \dfrac {2\pi}{7}+\sin \dfrac {4\pi}{7}+\sin \dfrac {8\pi}{7}$$ is

The value of $$\tan\theta+\sec\theta$$ is equal to

If $$\tan^{2}\alpha-\tan^{2}\beta-\dfrac{1}{2}\sin(\alpha-\beta)\sec^{2}\alpha\sec^{2}\beta$$ is zero then value of $$\sin(\alpha+\beta)$$ is $$(\alpha\neq\beta)$$

If $$cos\alpha+cos\beta+cos\gamma=sin\alpha+sin\beta+sin\gamma$$ then $$cos^2\alpha+cos^2\beta+cos^2\gamma=?$$

$$tan(\cfrac {1} {2} \sin^{-1} \cfrac {4} {5} + \cfrac {1} {2}cos^{-1} \cfrac {15} {17})$$ is equal to