Du findest auf
https://www.wolframalpha.com/input/?i=cos(x)+%2B+sin(x%2F2)*sin(x%2F2)+%3D+cos(x%2F2)
eine Step für Step Lösung, wenn du dich dort kostenlos registrierst. Dort sieht das auch besser aus als hier. Ich habe es nur mal mit cut & paste übernommen. Warum beim cut & paste die Ümbrücher verloren gehen weiß ich leider nicht :(
----------
Solve for x: cos(x)+sin^2(x/2) = cos(x/2) Move everything to the left hand side. Subtract cos(x/2) from both sides: cos(x)-cos(x/2)+sin^2(x/2) = 0 Simplify cos(x)-cos(x/2)+sin^2(x/2) = 0 by making a substitution. Simplify and substitute y = -cos(x/2): cos(x)+sin^2(x/2)-cos(x/2) = (-cos(1/2 x))^2-cos(1/2 x) = y^2+y = 0: y^2+y = 0 Factor the left hand side. Factor y from the left hand side: y (y+1) = 0 Solve each term in the product separately. Split into two equations: y = 0 or y+1 = 0 Look at the first equation: Perform back substitution on y = 0. Substitute back for y = -cos(x/2): -cos(x/2) = 0 or y+1 = 0 Multiply both sides by a constant to simplify the equation. Multiply both sides by -1: cos(x/2) = 0 or y+1 = 0 Eliminate the cosine from the left hand side. Take the inverse cosine of both sides: x/2 = pi/2+pi n_1 for n_1 element Z or y+1 = 0 Solve for x. Multiply both sides by 2: x = pi+2 pi n_1 for n_1 element Z or y+1 = 0 Look at the second equation: Solve for y. Subtract 1 from both sides: x = pi+2 pi n_1 for n_1 element Z or y = -1 Perform back substitution on y = -1. Substitute back for y = -cos(x/2): x = pi+2 pi n_1 for n_1 element Z or -cos(x/2) = -1 Multiply both sides by a constant to simplify the equation. Multiply both sides by -1: x = pi+2 pi n_1 for n_1 element Z or cos(x/2) = 1 Eliminate the cosine from the left hand side. Take the inverse cosine of both sides: x = pi+2 pi n_1 for n_1 element Z or x/2 = 2 pi n_2 for n_2 element Z Solve for x. Multiply both sides by 2: Answer: | | x = pi+2 pi n_1 for n_1 element Z or x = 4 pi n_2 for n_2 element Z
