Question

Verify the identity: [sin(3t)-sin(t)]/[cos(3t)+cos(t)]=tan(t)

Answer 1

For sin: sin(3t)*cos(t)-cos(3t)*sin(t)
For cos: cos(3t)*cos(t)-sin(3t)*sin(t)
Considering that, I want to say that this is not an identity.

Answer 2

sin3t=sin(2t+t)=sin2tcost+cos2tsint
cos3t=cos(2t+t)=cos2tcost-sin2tsint

Answer 3

plug them in the left side of the equation, you will get: