Question

доказать тождества
1)cos3x=4cos^3x-3cosx
2)sin3x=3sinx-4sin^3x

Answer 1

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