Use a sum of angles identity to solve sin(2x) cos (x) +cos(2x) sin(x) =sqrt 2/2

Question

sin(2x) cos(x) + cos(2x) sin(x) = √2

‾‾‾2‾‾‾‾ (√2 over 2)

Answer 1

sin(2x)cos(x)+sin(x)cos(2x) = sin(2x+x)= sin(3x) = √2/2

3x = sin^-1(√2/2) = π/4 +2πn or 3π/4 +2πn

x = π/12 + 2πn/3, π/4+2πn/3