Question

10 класс,алгебра,1 2 3 задание

Answer 1

1. $\frac{sin(\alpha + \beta) + sin(\alpha - \beta)}{cos(\alpha + \beta) + cos(\alpha - \beta)} = \frac{sin(\alpha) * cos(\beta) + sin(\beta) * cos(\alpha) + sin(\alpha) * cos(\beta) - sin(\beta) * cos(\alpha)}{cos(\alpha) * cos(\beta) - sin(\alpha)*sin( \beta) + cos(\alpha) * cos(\beta) + sin(\alpha)*sin( \beta)} = \frac{2sin(\alpha) * cos(\beta)}{2cos(\alpha) * cos(\beta)} = \frac{sin(\alpha)}{cos(\alpha)} = tg(\alpha)$2.

$2 *tg(105 ^\circ) = 2 * tg(45^\circ + 90^\circ) = 2 * \frac{tg(45^\circ) + tg(60^\circ)}{1 - tg(45^\circ) * tg(60^\circ)} = 2 * \frac{1 + \sqrt3}{1 - 1*\sqrt3} = 2 * \frac{(1 + \sqrt3)^2}{(1+\sqrt3)(1-\sqrt3)} = 2 * \frac{4 + 2\sqrt3}{-2} = -4-2\sqrt3$

3. $sin(40^\circ)*cos(22^\circ) + sin(22^\circ) * cos(40^\circ) - sin(62^\circ) = sin(62^\circ) - sin(62^\circ) = 0$