Question

Arrange the steps in the correct order to express cos3x in terms of cosx cos(2x)cos(x)-sin(2x)(x) [1-sin^2(x)]cos(x)-[2sin(x)cos(x)]sin(x) cos(x)-4sin^2(x)cos(x) 4cos^3(x)-3cos(x) cos(2x+x) cos(x){1-4[1-cos^2(x)]} cos(x)-2sin^2(x)cos(x)-sin^2(x)cos(x) cos(x)[1-4sin^2(x)] cos(x)[-3+4cos^2(x)]

Answer 1

cos(3x) = cos(2x+x)

= cos(2x) cos (x) -sin(2x)sin(x)

$=(1-2sin^2(x)) cos(x)-(2 sin(x) cos(x)) sin(x)$

$= cos x -2sin^2(x) cos(x) -2sin^2(x) cos(x)$

$= cos(x) - 4 sin^2(x) cos(x)$

$cos(x)(1-4sin^2(x))$

$=cos(x(1-4(1-cos^2(x))$

$=cos(x)(1-4+4cos^2(x))$

$= cos(x)-4cos(x)+4cos^3(x)$

$=-3cos(x)+4cos^3(x)$