$\displaystyle Sin 4\alpha = 4 Sin\alpha Cos\alpha Cos 2\alpha$
Hello, something3k!
Identity: .$\displaystyle 2\!\cdot\!\sin\theta\!\cdot\!\cos\theta \:=\:\sin2\theta$
Or start on the right side . . .$\displaystyle \sin4\alpha \:= \:4\!\cdot\!\sin\alpha\!\cdot\!\cos\alpha\!\cdot\! \cos2\alpha$
$\displaystyle 4\!\cdot\!\sin\alpha\!\cdot\!\cos\alpha\!\cdot\!\c os2\alpha \;=\;2\cdot\underbrace{2\!\cdot\!\sin\alpha\!\cdot \!\cos\alpha}_{\text{This is }\sin2\alpha}\cdot\cos2\alpha $
. . . . . . . . . . . . .$\displaystyle = \;\underbrace{2\!\cdot\!\sin2\alpha\!\cdot\!\cos2\ alpha} $
. . . . . . . . . . . . .$\displaystyle =\qquad \sin4\alpha $