When the coordinate axes are rotated through an angle 135$$\Upsilon$$, the coordinates of a point $$P$$ in the new system are known to be $$(4,-3)$$. Then find the coordinates of $$P$$ in the original system.

The maximum value of $$f(x)=\sin (x)$$ in the interval $$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$ is

$$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)$$ is equal to

If $$\sin \alpha - \cos \alpha = m$$ and $$\sin 2\alpha = n - {m^2}$$, where $$ - \sqrt 2 \le m \le \sqrt 2 $$, then n is equal to