Question

Prove : cos4x = 1 - 8cos²x + 8 cos^4 x​

Answer 1

Step-by-step explanation:

Cos4x = Cos(2*2x)

= 2Cos²2x - 1

= 2(2Cos²x-1)² - 1

= 2(4Cos⁴x-4Cos²x+1) - 1

= 8Cos⁴x - 8Cos²x + 2 - 1

= 1 - 8Cos²x + 8Cos⁴x

Ahead from here

= 1 - 8Cos²x(1-Cos²x)

= 1 - 8Cos²x*Sin²x

= 1 - 2(4Sin²x*Cos²x)

= 1 - 2Sin²2x