Ecuaciones Trigonometricas 1 Bachillerato — Ejercicios Resueltos

Use identity (\sin^2 x = 1 - \cos^2 x):

[ 2(1 - \cos^2 x) - \cos x - 1 = 0 ] [ 2 - 2\cos^2 x - \cos x - 1 = 0 ] [ -2\cos^2 x - \cos x + 1 = 0 ] Multiply by -1: [ 2\cos^2 x + \cos x - 1 = 0 ] Use identity (\sin^2 x = 1 - \cos^2

Let ( t = \cos x ): [ 2t^2 + t - 1 = 0 \implies t = \frac-1 \pm \sqrt1 + 84 = \frac-1 \pm 34 ] [ t_1 = \frac24 = \frac12,\quad t_2 = \frac-44 = -1 ] Use identity (\sin^2 x = 1 - \cos^2