Докажите равенство 2sin50°-1/(2sin70°)=1.

\[2\sin{50{^\circ}} - \frac{1}{2\sin{70{^\circ}}} = 1\]

\[\frac{2 \cdot \left( 2\sin{50{^\circ}} \cdot \sin{70{^\circ}} \right)}{2\sin{70{^\circ}}} = 1\]

\[1 + 2\cos{20{^\circ}} - 1 - 2\sin{70{^\circ}} = 0\]

\[2 \cdot \left( \cos\left( \frac{\pi}{2} - 70{^\circ} \right) - \sin{70{^\circ}} \right) = 0\]

\[\sin{70{^\circ}} - \sin{70{^\circ}} = 0\]

\[0 = 0\]