Use the identity sin^2x = 1 - cos(2x)/2 to obtain the Maclaurin series for sin2x. Then differentiate this series to obtain the Maclaurin series for 2sinxcosx. Check that this is the series for sin(2x). What is the Maclaurin series for sin2x? What is the Maclaurin series for 2sinxcosx = sin(2x)?
