Trigonometric F...

If $$cot\Theta =sin2\Theta (where\Theta \neq n\pi ,n\ is\ an\ integer)\Theta $$=

In a triangle ABC,

If $$\cos\ \theta+\sin\ \theta=a$$, then $$\sin\ 2\theta=$$

If $$\sin^{2} x- \cos x=1/4$$, then the value of $$x$$ between $$0$$ and $$2\pi$$ are :

$$\dfrac{1+cot\alpha+cosec\alpha}{1-cot\alpha+cosec \alpha}=$$

If $$\sin ^ { - 1 } x = y ,$$ then

The equation $$\sin x + \sin y + \sin z = -3$$ for $$0 \le x \le 2\pi, 0 \le y \le 2\pi, 0 \le z \le 2\pi$$, has

Number of solutions of the equation $$4\sin^{2}x+\tan^{2}x+\cot^{2}x+\csc^{2}=6$$ in $$[0, \pi]$$ is 

Number of solution of $$\tan ( 2 x ) = \tan ( 6 x ) \operatorname { in } ( 0,3 \pi )$$ is 

Solution of $$7 \sin ^ { 2 } x + 3 \cos ^ { 2 } x = 4$$ is