Question

Which is correct?

(a) sin 3x = 3sinx – 4sin^3x

(b) sin 3x = 4sinx – 3sin^3x

(c) sin 3x = 3sin^3x – 4sinx

(d) sin 3x = 4sin^3x – 3sinx

This question was addressed to me in an online quiz.

The query is from Trigonometric Functions of Sum and Difference of Two Angles-2 topic in chapter Trigonometric Functions of Mathematics – Class 11

Answer 1

The correct option is (a) sin 3x = 3sinx – 4sin^3x

Explanation: sin 3x = sin (2x + x)

= sin 2x cos x + cos 2x sin x

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

= 2 sin x (1 – sin^2 x) + sin x – 2 sin^3 x

= 2 sin x – 2 sin^3 x + sin x – 2 sin^3 x

= 3 sin x – 4 sin^3 x.