+129850 (a) 4 sinx + 3cos(x + pi/3) = 2
4sinx + 3 [ cosxcos(pi/3) - sinxsin(pi/3)] = 2
4sinx + [3/2]cosx - (3*sqrt(3)/2)sinx = 2
8sinx + 3cosx - 3sqrt(3) sinx = 4
[8 - 3sqrt(3)]sinx - 4 = 3cosx square both sides
[91 - 48*sqrt(3)]sin^2x - [64 - 24*sqrt(3)] sinx + 16 = 9[cos^2x]
[91 - 48*sqrt(3)]sin^2x - [64 - 24*sqrt(3)] sinx + 16 = 9 - 9sin^2x
[100 - 48*sqrt(3)]sin^2x - [64 - 24*sqrt(3)] sinx + 7 = 0
Let a = sinx and we have
[100 - 48*sqrt(3)]a^2 - [64 - 24*sqrt(3)] a + 7 = 0
And using the quadratic formula, we have
a = 1/2 so sinx = 1/2 and this happens at pi/6 rads
or
a ≈ .83029 so sinx ≈ .83029 and, taking the sine inverse of .83029, this occurs at about .9796 rads
Here's a graph that confirms both results : https://www.desmos.com/calculator/dl9hzyg9b0
