Question

How do you use the formulas for sin (A +- B) and cos (A +-B) to prove the double angle formulas for sin 2A and cos 2A?

Answer 1

Use the fact that `2A` = `A+A`.

`sin(2A) = sin(A+A) = sinAcosA+sinAcosA = 2sinAcosA`

`cos(2A) = cos(A+A) = cosAcosA-sinAsinA`

And so on.