Smalltalk

2*cos (2*x) - sin (x) = -1 |2 ausklammern
2*(1-2*sin²(x)) - sin (x) = -1
2-4*sin²(x) - sin (x) = -1 |-2
-4*sin²(x) - sin (x) = -3 |:[-4]
sin²(x) + 1/4*sin*(x) = 3/4 | -3/4
sin²(x)+1/4*sin (x) - 3/4 = 0
(sin (x) + 1/8)² - 1/64 - 3/4 = 0 |+49/64
(sin (x) + 1/8)² = 49/64 | Wurzel ziehen
sin (x) + 1/8 = 7/8 oder sin (x) + 1/8 = -7/8 |-1/8
sin(x) = 6/8 oder sin (x) = -1
x=48,59037789 oder x = -90