Question

Which is correct?

(a) cos 3x = 3cosx – 4cos^3x

(b) cos 3x = 4cosx – 3cos^3x

(c) cos 3x = 3cos^3x – 4cosx

(d) cos 3x = 4cos^3x – 3cosx

I got this question by my school teacher while I was bunking the class.

This is a very interesting question from Trigonometric Functions of Sum and Difference of Two Angles-2 topic in division Trigonometric Functions of Mathematics – Class 11

Answer 1

The correct option is (d) cos 3x = 4cos^3x – 3cosx

Easy explanation: cos 3x = cos (2x +x)

= cos 2x cos x – sin 2x sin x

= (2cos^2 x – 1) cos x – 2sin x cos x sin x

= (2cos^2 x – 1) cos x – 2cos x (1 – cos^2 x)

= 2cos^3 x – cos x – 2cos x + 2 cos^3 x

= 4cos^3 x – 3cos x.