Verify tanxsin2x = 2-2cos^2x

Answer 1

tan(x) = sin(x) / cos(x)

sin(2x) = 2 * sin(x) * cos(x)

tan(x)*sin(2x) = [sin(x) / cos(x)] * 2 * sin(x) * cos(x) =

2 sin(x) * sin(x) = 2 sin^2(x)

sin^2(x) + cos^2(x) = 1

sin^(x) = 1 - cos^2(x)

2 sin^2(x) = 2 * [ 1 - cos^2(x) ] = 2 - 2 * cos^2(x)