If $A+B=225^{\circ}$,then the value of $\frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B}$ is equal to

The maximum value of $\sin \left( x + \frac{\pi}{6} \right) + \cos \left( x + \frac{\pi}{6} \right)$ in the interval $\left( 0, \frac{\pi}{2} \right)$ is attained at

Let $f(\theta) = (1 + \sin^2 \theta)(2 - \sin^2 \theta)$. Then, for all values of $\theta$:

If the range of $f(\theta) = \frac{\sin^4 \theta + 3 \cos^2 \theta}{\sin^4 \theta + \cos^2 \theta}$,$\theta \in R$ is $[\alpha, \beta]$,then the sum of the infinite $G.P.$,whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$,is equal to...........

The minimum value of $2 \sin^2 \theta + 8 \csc^2 \theta$ is (where $\theta \in R$):-

If $K = \sin^6x + \cos^6x$,then $K$ belongs to the interval