prove two equations containing sinusoids are equal

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given two sinusoids of the same frequence
Vx(t)= Csin(wt)
Vy(t)= D(sinwt + a)

show that,
Vx^2/C^2 + Vy^2/D^2 - (2VxVycos(a))/(CD)= (sin(a))^2

note, Vx is V sub x, and Vy is V sub y

I know I have to use the trig identities sin(a+B)=sin(a)cos(b)+sin(b)cos(a)
and sin(a)^2+cos(a)^2=1
but plugging all of that in there and expanding is a bit complicated.
 
blast said:
given two sinusoids of the same frequence
Vx(t)= Csin(wt)
Vy(t)= D(sinwt + a)

show that,
Vx^2/C^2 + Vy^2/D^2 - (2VxVycos(a))/(CD)= (sin(a))^2

note, Vx is V sub x, and Vy is V sub y

I know I have to use the trig identities sin(a+B)=sin(a)cos(b)+sin(b)cos(a)
and sin(a)^2+cos(a)^2=1
but plugging all of that in there and expanding is a bit complicated.
Click to expand...

I don't see how you would use the sin(a+B) identity...

That is, unless you meant Vy=Dsin(wt+a)
 
oops yea thats what I meant..
anyways, I figured out the problem so thanks anyways.
 
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