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# Prove the following: cos 4x = 1 - 8sin²x cos²x

**Solution:**

LHS = cos 4x

= cos 2(2x)

= 1 - 2sin^{2}2x [By double angle formulas, cos 2A = 1 - 2sin^{2}A]

= 1 - 2(2sin x cos x)^{2} [By double angle formulas, sin 2A = 2sin A cos A]

= 1 - 2(4sin^{2}xcos^{2}x)

= 1 - 8sin^{2}x cos^{2}x

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 24

## Prove the following: cos 4x = 1 - 8sin²x cos²x

**Summary:**

We got, cos 4x = 1 - 8sin^{2}x cos^{2}x. Hence Proved

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