Trigonometric F...

The no of solution of the equation: $$1+\sin { x } \cos { x } =2\sin { x } \cos { x } $$ in $$x$$, $$\left[ 0,40 \right] $$ are

$$\sin^2 20+\sin^270$$ is equal to_____

Find number of solutions to the equation:$$\left[ \sin { x+\cos { x }  }  \right] =3+\left[ -\sin { x }  \right] +\left[ -\cos { x }  \right]$$

The number of solutions of the equation $$|\cot x|=\cot x+\dfrac{1}{\sin x}(0\le x\le 2\pi)$$ is :

If $$\cos 3x=-1$$, where $$0^{o} \ge x \ge 360^{o}$$, then $$x$$

Solution set of the equation $$\sin ^{ 2 }{ x } +\cos ^{ 2 }{ 3x }$$ =1$$ is given by 

If $$\theta$$ is an acute angle such that $$\sec^2 \theta = 3$$. then the value of $$\dfrac{\tan^2 \theta - \text{cosec}^2 \theta}{\tan^2 \theta - \text{cosec}^2 \theta}$$ is 

For $$x\ \in\ (0,\pi)$$, the equation $$\sin x+2\sin 2x-\sin 3x=3$$ has

The number of value of $$x\in (0,2\pi)$$ satisfying $$\log_{\tan x}(2+4\cos^2x)=2$$

The sum $$s=sin\theta+sin2\theta+.......+sin n \theta$$, equals