Trigonometry problem

hatter98:

cos(x)-4sin^2(x)cos(x)=cos(3x)

Why?

cos(x)-4sin ²(x)cos(x)=cos(3x)

RHS=cos(3x)

=cos(x+2x)

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

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

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

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

=cos(x)[ 1 - sin ²(x) - sin ²(x) - 2sin ²(x) ]

=cos(x)[1 - 4sin ²(x) ]

=cos(x) - 4sin ²(x)cos(x)

=LHS