The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is
$2n\pi + \frac{\pi }{3},\,n \in I$
$n\pi + \frac{\pi }{2},\,n \in I$
$n\pi + \frac{\pi }{4},\,n \in I$
$2n\pi - \frac{\pi }{3},\,n \in I$
The equation $5x^2+12x + 13 = 0$ and $ax^2+bx + c = 0$ have a common root, where $a,b,c$ are the sides of $\Delta ABC$,then find $\angle C$ ? .....$^o$
If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is
If the equation $2\ {\sin ^2}x + \frac{{\sin 2x}}{2} = k$ , has atleast one real solution, then the sum of all integral values of $k$ is
If the solution for $\theta $ of $\cos p\theta + \cos q\theta = 0,\;p > 0,\;q > 0$ are in $A.P.$, then the numerically smallest common difference of $A.P.$ is
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is