Prove the following: cos 6x = 32cos⁶x - 48cos⁴x + 18cos²x - 1

Solution:

LHS = cos 6x

= cos 3(2x)

= 4cos³2x - 3cos2x     [As cos 3A = 4cos³A - 3cosA]

= 4(2cos²x - 1)³ - 3(2cos²x - 1)     [By double angle formula, cos 2A = 2cos²A - 1]

= 4(8cos⁶x - 1 - 12cos⁴x + 6cos²x) - 6cos²x + 3     [Because (a - b)³ = a³ - b³ - 3a²b+ 3ab²]

= 32cos⁶x - 4 - 48cos⁴x + 24cos²x - 6cos²x + 3

= 32cos⁶x - 48cos⁴x + 18cos²x - 1

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 25

Prove the following: cos 6x = 32cos⁶x - 48cos⁴x + 18cos²x - 1

Summary:

We got, cos 6x = 32cos⁶x - 48cos⁴x + 18cos²x - 1. Hence Proved