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 only value of $x$ for which $2^{\sin x} + 2^{\cos x} > 2^{1 - (1/\sqrt{2})}$ holds,is

Find the maximum and minimum values of the function given by $h(x) = \sin(2x) + 5$.

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3$,then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 =$

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^2$,where $f(\theta)=\sqrt{a^2 \cos^2 \theta+b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta+b^2 \cos^2 \theta}$. Then $M-m=$

$a, b, c$ are the sides of a scalene triangle $ABC$. If angles $\alpha, \beta, \gamma$ lie between $0$ and $\pi$ such that $\cos \alpha = \frac{a}{b+c}, \cos \beta = \frac{b}{c+a}$ and $\cos \gamma = \frac{c}{a+b}$,then $\tan^2 \frac{\alpha}{2} + \tan^2 \frac{\beta}{2} + \tan^2 \frac{\gamma}{2} =$