How do you verify the identity: cotx=sin3x+sinxcos3xcosx?

1 Answer
Feb 6, 2015

There are some formulas, named sum-to-product, that say:

sinθ+sinϕ=2sin(θ+ϕ2)cos(θϕ2),
sinθsinϕ=2cos(θ+ϕ2)sin(θϕ2),
cosθ+sinϕ=2cos(θ+ϕ2)cos(θϕ2),
cosθ+cosϕ=2sin(θ+ϕ2)sin(θϕ2).

So:

cotx=2sin(3x+x2)cos(3xx2)2sin(3x+x2)sin(3xx2);

cotx=cosxsinx.

That's all.