Question

Sin 3x = 3sinx - 4sin3x

Answer 1

Answer:

sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta

and the double angle formula of cosine:

cos(2alpha)=cos^2alpha-sin^2alpha=2cos^2alpha-1=1-2sin^2alpha#

then:

sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx=#

=(2sinxcosx)*cosx+(1-2sin^2x)sinx=#

=2sinxcos^2x+sinx-2sin^3x=#

=2sinx(1-sin^2x)+sinx-2sin^3x=#

=2sinx-2sin^3x+sinx-2sin^3x=#

=3sinx-4sin^3x#.