Докажите тождество sin (2a) = sin (2b), если tga*tgb=1

Sin (2a) = sin (2b) - > 2sin (a) cos (a) = 2sin (b) cos (b) - > sin (a) cos (a) = sin (b) cos (b)

если tg (a) = tg (b), то sin (a) * sin (b) / (cos (a) * cos (b)) = 1, то sin (a) * sin (b) = cos (a) * cos (b)