Trigonometric F...

If $$\mathrm{s}in(\pi \mathrm{c}\mathrm{o}s\theta)= \mathrm{c}os$$$$(\pi\sin\theta)$$ , then which of the following is correct

 If $$\tan\theta=\displaystyle \dfrac{x\sin\phi}{1-x\cos\phi}$$, $$\displaystyle \tan\phi=\dfrac{y\sin\theta}{1-y\cos\theta}$$ , then $$\displaystyle \dfrac{x}{y}=$$

If $$ 32\tan^{8}\theta=2\cos^{2}\alpha-3\cos\alpha$$ and $$3\cos2\theta=1$$ then the general value of $$\alpha$$ is

The values of $$x$$ between $$0$$ and $$2p$$ which satisfy the equation $$\sin x\sqrt{8\cos^{2}x}=1$$ are in A.P. The common difference of the A.P. is

$$|\tan x + \sec x| = |\tan x| - |\sec x|, x \epsilon [0,2\pi]$$if and only if x belongs to the interval

The total number of solutions of $$\cos x=\sqrt{1-\sin 2x}$$ in $$\left [ 0,2\pi  \right ]$$ is equal to

Find the value of $$\cot^{-1}\left(\dfrac{\sqrt {1-\sin x}+\sqrt {1+\sin x}}{\sqrt {1-\sin x}-\sqrt {1+\sin x}}\right)$$

The difference between greatest and least solution of $$x$$ is-

The value of $$\dfrac{\tan \alpha}{1-\cot \alpha}+\dfrac{\cot \alpha}{1-\tan \alpha}$$ is identically equal to

If $$ \cos \theta - \sin \theta =\sqrt{2} \sin \theta$$, then $$ \cos \theta + \sin \theta$$ is