Question

Вычислите sin30 + cos60 - sin135 * sin135

Answer 1

sin30° = 0,5

cos60° = 0,5

sin135° = √2/2

0,5 + 0,5 - (√2/2)^2 = 1 - 2/4 = 1 - 1/2 = 0,5

Answer 2

$\sin(30\textdegree) + \cos(60\textdegree) - \sin(135\textdegree) \times \sin(135\textdegree) = \\ = \sin(30\textdegree) + \cos(60\textdegree) - \sin ^{2} (135\textdegree)$

$\sin(30\textdegree) = \frac{1}{2} \\ \cos(60\textdegree) = \frac{1}{2} \\ \sin(135\textdegree) = \sin(90\textdegree+45\textdegree) = \cos(45\textdegree) = \frac{ \sqrt{2} }{2}$

$\frac{1}{2} + \frac{1}{2} - (\frac{ \sqrt{2} }{2} ) ^{2} = 1 - \frac{2}{4} = 1 - \frac{1}{2} = \frac{1}{2}$