Trigonometry Question (1 Viewer)

[phoenix159]

Help needed with a trigonometry question:

Show that: cos 3x = 4 cos³x - 3 cos x

I expanded the LHS using the sum of 2 angles and got


cos 3x = cos³x - 3cos x sin x

 

[HeroicPandas]

cos 3x = cos (2x + x)

Now,

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

Let c = cosx, s = sinx

= (2c^2 - 1)c - 2s^2 c (utilising sine and cosine double angles)

= 2c^3 - c - 2c(1-c^2) (apply pythagorean identity of s^2 + c^2 = 1)

= 4c^3 - 3c^2

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

= RHS