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# Prove the following: (sin x - sin 3x) / (sin^{2}x - cos^{2}x) = 2sin x

**Solution:**

LHS = (sin x - sin 3x) / (sin^{2}x - cos^{2}x)

= [2cos (x + 3x)/2 sin (x - 3x)/2] / -[cos^{2}x - sin^{2}x]

[Since sin A - sin B = 2 cos [(A + B) / 2] sin [(A - B) / 2]]

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

[By double angle formulas, cos 2x = cos^{2}x - sin^{2}x ]

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

[As sin (-A) = - sin A]

= 2sin x

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 20

## Prove the following: (sin x - sin 3x) / (sin²x - cos²x) = 2sin x

**Summary:**

We got, (sin x - sin 3x) / (sin^{2}x - cos^{2}x) = 2sin x. Hence Proved

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