The value of $k$, for which ${(\cos x + \sin x)^2} + k\,\sin x\cos x - 1 = 0$ is an identity, is
$-1$
$-2$
$0$
$1$
If $\theta $ lies in the second quadrant, then the value of $\sqrt {\left( {\frac{{1 - \sin \theta }}{{1 + \sin \theta }}} \right)} + \sqrt {\left( {\frac{{1 + \sin \theta }}{{1 - \sin \theta }}} \right)} $
If $\tan \theta = \frac{{x\,\sin \,\phi }}{{1 - x\,\cos \,\phi }}$ and $\tan \,\phi = \frac{{y\sin \,\theta }}{{1 - y\,\cos \,\theta }}$, then $\frac{x}{y} = $
If $\cos \theta = \frac{1}{2}\left( {x + \frac{1}{x}} \right)$, then $\frac{1}{2}\left( {{x^2} + \frac{1}{{{x^2}}}} \right) = $
If $\cos \theta - \sin \theta = \sqrt 2 \sin \theta ,$ then $\cos \theta + \sin \theta $ is equal to
If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.