Trigonometric F...

If $$\cos ^{ -1 }{ \left( \cfrac { p }{ a }  \right)  } +\cos ^{ -1 }{ \left( \cfrac { p }{ b }  \right)  } =\alpha $$, then $$\cfrac { { p }^{ 2 } }{ { a }^{ 2 } } +k\cos { \alpha  } +\cfrac { { p }^{ 2 } }{ { b }^{ 2 } } =\sin ^{ 2 }{ \alpha  } $$, where $$k$$ is equal to

If $$\cos { \alpha  } +\cos { \beta  } +\cos { \gamma  } =\sin { \alpha  } +\sin { \beta  } +\sin { \gamma  } =0$$, then the value of $$\cos { 3\alpha  } +\cos { 3\beta  } +\cos { 3\gamma  } $$ is

If $$2\sin^{2}\theta + \sqrt {3}\cos \theta + 1 = 0$$, then the value of $$\theta$$ is

The set of values of a for which the equation $$\sin x(\sin x+\cos x)=a$$ has real solutions is

The value of $$\cos ^{ 4 }{ \left( \cfrac { \pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 3\pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 5\pi  }{ 8 }  \right)  } +\cos ^{ 4 }{ \left( \cfrac { 7\pi  }{ 8 }  \right)  } $$ is

Which one of the following equations has no solution?

One of the principal solutions of $$ \sqrt3 \sec x = - 2 $$ is equal to :

The number of solutions of the equation $$\sin\theta +\cos\theta =\sin 2\theta$$ in the interval $$[-\pi, \pi]$$ is?

Let $$X = \left \{x\epsilon \mathbb {R} : \cos (\sin x) = \sin (\cos x)\right \}$$. The number of solutions of $$X$$ is?

The number of real solutions of the equation $$2\sin 3x+\sin 7x-3=0$$ which lie in the interval $$[-2\pi, 2\pi]$$ is?