$cosec^2\theta $ = $\frac{4xy}{(x +y)^2}$ is true if and only if
$x + y$ $\neq$ $0$
$x = y$, $x$ $\neq$ $0$
$x = y$
$x$ $\neq$ $0$, $y$ $\neq$ $0$
If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is
If $\cos x + \cos y + \cos \alpha = 0$ and $\sin x + \sin y + \sin \alpha = 0,$ then $\cot \,\left( {\frac{{x + y}}{2}} \right) = $
If $\tan \beta = \cos \theta \tan \alpha ,$ then ${\tan ^2}\frac{\theta }{2} = $
Suppose $\theta $ and $\phi (\ne 0)$ are such that $sec\,(\theta + \phi ),$ $sec\,\theta $ and $sec\,(\theta - \phi )$ are in $A.P.$ If $cos\,\theta = k\,cos\,( \frac {\phi }{2})$ for some $k,$ then $k$ is equal to
If $A$ lies in the third quadrant and $3\ tanA - 4 = 0$ , then find the value of $5\ sin\ 2A + 3\ sinA + 4\ cosA$