Sum-to-Product

[nycmathguy]

Section 5.5

 

[MathLover1]

sin(3theta)+sin(theta)

sin(u)+sin(v) =2sin(u/2 + v/2) cos(u/2 - v/2) where u=3theta and v=theta

=2sin(3theta/2 + theta/2) cos(3theta/2 - theta/2)

=2sin(2theta) cos(theta).......sin(2theta)=2sin(θ) cos(θ)

=2(2sin(θ) cos(θ)) cos(theta).

=4sin(θ) cos^2(θ)

 

[nycmathguy]

sin(3theta)+sin(theta)

sin(u)+sin(v) =2sin(u/2 + v/2) cos(u/2 - v/2) where u=3theta and v=theta

=2sin(3theta/2 + theta/2) cos(3theta/2 - theta/2)

=2sin(2theta) cos(theta).......sin(2theta)=2sin(θ) cos(θ)

=2(2sin(θ) cos(θ)) cos(theta).

=4sin(θ) cos^2(θ)

Wrong again, right?
If so, I may do 53 and 55.

 

[nycmathguy]

sin(3theta)+sin(theta)

sin(u)+sin(v) =2sin(u/2 + v/2) cos(u/2 - v/2) where u=3theta and v=theta

=2sin(3theta/2 + theta/2) cos(3theta/2 - theta/2)

=2sin(2theta) cos(theta).......sin(2theta)=2sin(θ) cos(θ)

=2(2sin(θ) cos(θ)) cos(theta).

=4sin(θ) cos^2(θ)

 

[MathLover1]

53. correct, you can just stop on line 2 sin( θ) cos(4 θ), no need to go further
55. correct

 

[nycmathguy]

53. correct, you can just stop on line 2 sin( θ) cos(4 θ), no need to go further
55. correct

Thank goodness I got it right.