cos(x+60)=2sinx

cos(a+b) = cos a cos b - sin a sin b

 

cosxcos60 - sinxsin60 = 2 sin x

1/2 cosx - sqrt3/2 sinx = 2 sinx

1/2 cos x = 2+ sqrt3/2) sin x

cos x = ( 4 + sqrt3)sinx

tan x = 1/ (4 + sqrt3 )

x = arc tan[1/ (4 + sqrt3)] = 9.896 degrees