sin-2-x-4cos-3-x-1-2cos-2-x-2cos-x-2cos-xsin-2-x-x-

Question Number 145979 by iloveisrael last updated on 09/Jul/21

\sin^{2} x - 4 \cos^{3} x - 1 = 2 \cos^{2} x + 2 \cos x - 2 \cos xsin^{2} x

x = ?

Answered by Olaf_Thorendsen last updated on 10/Jul/21

\sin^{2} x - {4 \cos}^{3} x - 1 = {2 \cos}^{2} x + 2 \cos x - 2 \cos x \sin^{2} x

Let X = \cos x

1 - X^{2} - {4 X}^{3} - 1 = {2 X}^{2} + 2 X - 2 X (1 - X^{2})

- {6 X}^{3} - {3 X}^{2} = 0

X^{2} (2 X + 1) = 0

X = \cos x = 0 \Leftrightarrow x = \pm \frac{π}{2} + 2 k π

X = \cos x = - \frac{1}{2} \Leftrightarrow x = \pm \frac{2 π}{3} + 2 k π