If $\cos 2\theta = (\sqrt 2 + 1)\,\,\left( {\cos \theta - \frac{1}{{\sqrt 2 }}} \right)$, then the value of $\theta $ is
$2n\pi + \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
$2n\pi - \frac{\pi }{4}$
None of these
The equation $\sin x\cos x = 2$ has
The smallest positive values of $x$ and $y$ which satisfy $\tan (x - y) = 1,\,$ $\sec (x + y) = \frac{2}{{\sqrt 3 }}$ are
The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is
The set of all values of $\lambda$ for which the equation $\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda$
If $\cos {40^o} = x$ and $\cos \theta = 1 - 2{x^2}$, then the possible values of $\theta $ lying between ${0^o}$ and ${360^o}$is