If $$x+y=\frac{\pi}{2}$$, then the maximum value of $$\sin x \cdot \sin y$$ is

If $$a=\sin 175^{\circ}+\cos 175^{\circ}$$, then

The polar co-ordinates of the point whose cartesian co-ordinates are $$(-2,-2)$$, are given by

If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$