$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to
$tan\,2^{99} -tan\,1$
$tan\,2^{100}$
$tan\,2^{100} -tan\,1$
none of these
$sin^{2n}x + cos^{2n}x$ lies between
If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
The number of solutions of the equation $sin\, 2x - 2\,cos\,x+ 4\,sin\, x\, = 4$ in the interval $[0, 5\pi ]$ is
The number of solutions of the given equation $\tan \theta + \sec \theta = \sqrt 3 ,$ where $0 < \theta < 2\pi $ is