Trig Identity: Verify a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C)

[morr485]

1. Verify this identity: a*sin Bx + b*cos Bx = sqrt(a^2 + b^2)sin(Bx + C)
where C= arctan b/a
2. a/sqrt(a^2+b^2)sin Bx + b/sqrt(a^2+b^2)cos Bx=cos C sin Bx + sin C cos Bx=
3.a*sin Bx + b cos Bx = sqrt(a^2 + b^2) sin(Bx + C)

Homework Statement

Homework Equations

The Attempt at a Solution

 

[danago]

First thing that jumps to my mind is to make use of the trig expansion:

R sin(Bx+C)=R(sin(Bx) cos(C)+cos (Bx)sin(C))

 

[morr485]

danago thanks for the hint.