prove that sin 3theta = 3 sin theta - 4 sin cubed theta. confirm this identity for theta = pi/4

Question

dont know where to start on this

Answer 1

sin(3θ)=sin(2θ+θ)=sin(2θ)cos(θ)+cos(2θ)sin(θ)=

2sin(θ)cos²(θ)+(1-2sin²(θ))sin(θ)=

2sin(θ)(1-sin²(θ))+sin(θ)-2sin³(θ)=

3sin(θ)-4sin³(θ) QED

When θ=π/4, 3θ=3π/4 and sin(3π/4)=sin(π/4)=√2/2.

3sin(π/4)-4sin³(π/4)=3√2/2-4(2√2/8)=3√2/2-√2=√2/2 confirms the identity.

Comments

Thank you Rod your help is greatly appreciated.