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
${100^o}$ and ${260^o}$
${80^o}$ and ${280^o}$
${280^o}$ and ${110^o}$
${110^o}$ and ${260^o}$
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
$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $
If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ is-
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
If $r\,\sin \theta = 3,r = 4(1 + \sin \theta ),\,\,0 \le \theta \le 2\pi ,$ then $\theta = $