Question 1120455
cos 2x=2cos^2 x-1
2 cos 2x=4 cos^2 x-2
therefore, 4 cos^2 x-2=3-2cos x
4 cos^2 x+2 cos x-5=0.  Use quadratic formula
cos x=(1/8) (-2+/- sqrt 4+80)); sqrt (84)=9.165
cos x=(1/8)(7.165) and cos x= (1/8)(-11.165).  The second is <-1 and is not possible
the first is cos x=0.895625
x= arc cos 0.895625=26.4 degrees
check
cos 52.8 deg=0.605
2 cos 43.6=1.21
3-2 cos 26.4=3-2(0.605)=1.21

26.4 degrees