I did post it wrong.
sin(4x)/sin(x)=4cos(x)cos(2x).
Verify the identity, please explain!
3 answers
Please, keep the same name when posting on Jiskha.
It has already been explained. See Reiny's answer to your previous post.
For the left hand side, use
sin(4x)=2sin(2x)cos(2x)
sin(2x)=2sin(x)cos(x)
cos(2x)=cos²(x)-sin²(x)
and finally to eliminate sin²(x), use
sin²(x)=1-cos²(x)
For the right hand side, use
cos(2x)=cos²(x)-sin²(x)
and
sin²(x)=1-cos²(x)
Both sides will be expressed in terms of cos(x).
sin(4x)=2sin(2x)cos(2x)
sin(2x)=2sin(x)cos(x)
cos(2x)=cos²(x)-sin²(x)
and finally to eliminate sin²(x), use
sin²(x)=1-cos²(x)
For the right hand side, use
cos(2x)=cos²(x)-sin²(x)
and
sin²(x)=1-cos²(x)
Both sides will be expressed in terms of cos(x).
2 answers