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

Solution:

LHS = cos 4x

= cos 2(2x)

= 1 - 2sin²2x     [By double angle formulas, cos 2A = 1 - 2sin²A]

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

= 1 - 2(4sin²xcos²x)

= 1 - 8sin²x cos²x

= 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 - 8sin²x cos²x. Hence Proved