Trigonometric F...

If

The smallest positive number p for which the equation cos (p sin x) = sin (p cos x) has a solution in $$[0, 2 \pi]$$ is 

If $$sin \alpha + sin \beta = \dfrac{1}{2} $$ and $$cos \alpha + cos \beta = \dfrac{\sqrt{3}}{2}$$ then $$3 \beta + \alpha = $$

In $$\Delta ABC, \sum \dfrac{b^2 - c^2}{a^2} sin \, 2A$$ = 

$$[3(\sin(\cos\ 1)+\cos(\cos\ 1))]$$ is equal to (where[.] is denotes the greatest integer function)

If $$sin\alpha sin \beta  - cos \alpha  \beta  - 1,  = 0$$ then the value of  $$cot \alpha  tan \beta $$  is 

If $$x=\sin\alpha+\sin\beta$$ and $$y=\cos\alpha+\cos\beta$$
then $$x=\tan\alpha+\tan\beta=$$

The value of $$\csc \dfrac{\pi}{13}-\sqrt{3} \sec \dfrac{\pi}{18}$$ is a 

If $$\cos^{2} \theta + 3\cos^{2}\theta + 4\sin^{2}\theta + .... (200) terms = 10025$$, where $$\theta$$ is an acute angle, then the value of $$\sin \theta - \cos \theta$$ is

The number of solution of the equation $${x^3} + 2{x^2} + 5x + 2\cos x = 0\,in\,[0,2\pi ]$$ is