Answer:
α = π/3
γ = 2
x = -3π/4, -5π/12, π/4, 7π/12
Explanation:
Easiest way to do this is in reverse.
γ sin(2x − α)
Angle sum/difference formula:
γ (cos α sin(2x) − sin α cos(2x))
Distribute:
γ cos α sin(2x) − γ sin α cos(2x)
Matching the coefficients:
γ cos α = 1
γ sin α = √3
Solve the system of equations. Divide to eliminate γ:
tan α = √3
α is between 0 and π/2, so:
α = π/3
γ = 2
sin(2x) − √3 cos(2x) = 1
Using the identity from before:
2 sin(2x − π/3) = 1
Solving:
sin(2x − π/3) = 1/2
2x − π/3 = π/6 + 2kπ or 5π/6 + 2kπ
2x = π/2 + 2kπ or 7π/6 + 2kπ
x = π/4 + kπ or 7π/12 + kπ
x is between -π and π, so:
x = -3π/4, -5π/12, π/4, 7π/12