Доказать тождества

1) cos3x=4cos^3x-3cosx

2) sin3x=3sinx-4sin^3x

1) cos3x = cos (2x+x) = cos2x cosx - sin2x sinx =

= (2cos^2 x - 1) cosx - 2sinx cosx sinx x = 2cos^3 x - cosx - 2sin^2 x cosx =

= 2cos^3 x - cosx - 2cosx + 2cos^3 x = 4cos^3 x - 3cosx

2) sin3x = sin (2x + x) = sin2x cosx + cos2x sinx =

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

= 2sinx - 2sin^3 x + sinx - 2sin^3 x = 3sinx - 4sin^3 x