Question

Prove that : cos 3x = 4 cos³x - 3 cos x​

Answer 1

Explanation:

Apply the trig identities:

cos(a+b)=cosa⋅cosb−sina⋅sinb

cos2x=2cos^2x−1

sin2x=2sinx⋅cosx

We get:

cos3x=cos(x+2x)=cosx⋅cos2x−sinx⋅sin2x

=cosx(2cos^2x−1)−2sin^2x⋅cosx

=2cos^3x−cosx−2cosx(1−cos^2x)

=2cos^3x−cosx−2cosx+2cos^3x

So,. cos3x=4cos^3x−3cosx