2. Use the angle doubling formula: sin2c = 2 sinc cosc, cos2c = 1-2 (sinc) 2.
3. Use the formula: (COSD) 2 = 1-(SIND) 2.
[proof]
sin3x
=sin(2x+x)
=sin2xcosx+cos2xsinx
=(2sinxcosx)cosx+[ 1-2(sinx)^2]sinx
=2sinx(cosx)^2+sinx-2(sinx)^3
=2sinx[ 1-(sinx)^2]+sinx-2(sinx)^3
=3sinx-4(sinx)^3,
∴4(sinx)^3=3sinx-sin3x,∴(sinx)^3=(3/4)sinx-( 1/4)sin3x。