For what value of θ does sin 2θ = cos (θ + 30)

Question

I need this answer for some homework, but I don't understand how to do it exactly. I'm in trigonometry.

Answer 1

sin 2θ = cos (θ + 30)

let put into radians, sin 2θ = cos (θ + π/6)

can write sin(π/2- (θ + π/6))=cos (θ + π/6)

now have sin 2θ=sin(π/3-θ)

2θ₁=π/3- θ₁+2πk where k=0,+/-1,+/-2,...

2θ₂=π-(π/3- θ₂)+2πk where k=0,+/-1,+/-2,...

It should check out

for solutions when k=0, does sin(2θ)=sin(π/3-θ)?