Here's a visual proof that
sin2x = 2sinxcosx
cos2x = cos²x−sin²x pic.twitter.com/vC9jVTsZT1

— Fermat's Library (@fermatslibrary) October 31, 2020

Visual proof of the addition formulas

sin(α+β)=sin(α)cos(β)+cos(α)sin(β)

cos(α+β)=cos(α)cos(β)–sin(α)sin(β) pic.twitter.com/OL7VwEgKZ5

— Tamás Görbe (@TamasGorbe) March 4, 2019