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

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

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

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