Question

HELP ON THIS PROBLEM!! Solve the following 0deg< x< 360deg: cos x= cos 2x

Answer 1

Answer:

$x=0^\circ,120^\circ,240^\circ,360^\circ$

Step-by-step explanation:

Use identities to set the equation up as a quadratic

$\cos x=\cos 2x;\:0^\circ \leq x \leq 360^\circ\\\\\cos x=2\cos^2 x-1\\\\0=2\cos^2 x-\cos x-1$

Make the substitution u=cos(x) and solve the quadratic

$0=2u^2-u-1\\\\0=(2u+1)(u-1)$

$\displaystyle 0=2u+1\\\\0=2\cos x+1\\\\-1=2\cos x\\\\-\frac{1}{2}=\cos x\\\\120^\circ,240^\circ=x$

$0=u-1\\\\0=\cos x-1\\\\1=\cos x\\\\0^\circ,360^\circ=x$

Hence, $x=0^\circ,120^\circ,240^\circ,360^\circ$