Trigonometric F...

$$9\tan^{2}\theta - 9 \sec^{2}\theta =$$

If $$\sin( \pi \cos \theta) = \cos (\pi \sin \theta)$$, then which of the following is correct.

The number of principal solutions of $$\tan 2\theta = 1$$ is

The equation $$ \sqrt {3} \sin x + \cos x = 4 $$ has 

Principal solutions of the equation $$\sin { 2x } +\cos { 2x } =0$$, where $$\pi< x< 2\pi$$ are

The number of solutions $$\left[ \cos { x }  \right] +\left| \sin { x }  \right| =1$$ in $$\pi \le x < 3\pi $$, where $$[x]$$ is the greatest integer not exceeding $$x$$ is

Principal solutions of the equation $$\sin 2x+\cos2x=0$$, where $$\pi < x < 2\pi$$ are

$$\displaystyle \left ( 1+\cot^{2}\theta \right )\left ( 1-\cos\theta \right )\left ( 1+\cos\theta \right )=$$

The number of roots of the equation $$x + 2\tan x = \dfrac {\pi}{2}$$ in the interval $$[0, 2\pi]$$ is

If $$0\le x\le 2\pi $$, then the number of solutions of the equation $$\sin ^{ 6 }{ x } +\cos ^{ 6 }{ x } =1$$ is