The value of $k$,for which $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0$ is an identity,is

From two points,lying on the same horizontal line,the angles of elevation of the top of the pillar are $\theta$ and $\phi$ $(\theta < \phi)$. If the height of the pillar is $h$ $m$ and the two points lie on the same side of the pillar,then the distance between the two points is (in $m$):

$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}$ is equal to

Number of integral values of $\lambda$ for which $f(x) = \sqrt{\ln(2\lambda \cos x + 5)}$ is defined for all $x \in R$ is

If $7 \sin^{2} \theta + 3 \cos^{2} \theta = 4$,then the value of $\tan \theta$ is (where $\theta$ is acute).

If $(\sin \alpha + \operatorname{cosec} \alpha)^{2} + (\cos \alpha + \sec \alpha)^{2} = K + \tan^{2} \alpha + \cot^{2} \alpha$,then the value of $K$ is