Question

Докажите тождество : 4sina cosa × cos2a=sin4a

Answer 1

$4 \sin(a) \cos(a) \times \cos(2a) = \sin(4a) \\ \\ 4 \sin(a) \cos(a) \times \cos(2a) = 2 \times 2\sin(a) \cos(a) \times \cos(2a) = \\ = 2 \sin(2a) \cos( 2a ) = \sin(2 \times 2a) = \sin(4a) \\ \\ \sin(4a) = \sin(4a)$