Prove cos 4x = 8 cos4x − 8 cos2x + 1.

Answer 1

Prove: cos 4x = 8 cos4x − 8 cos2x + 1 <== I think there is typo issue here. I think, it is:

Prove: cos 4x = 8 cos⁴x − 8 cos²x + 1 <== cos 4x = 8 (cos x)⁴ − 8 (cos x)² + 1 <== I will Prove this

Prove by starting at Left Hand Side (cos 4x) and arrive to Right Hand Side (8 cos⁴x − 8 cos²x + 1)

cos 4x = cos 2(2x) = 2 cos²2x - 1 = 2 (cos 2x)² - 1 = 2 (2 cos²x - 1)² - 1 = 2 (4 cos⁴x - 4 cos²x + 1) - 1 = 8 cos⁴x - 8 cos²x + 2) - 1 = 8 cos⁴x - 8 cos²x + 2 - 1 = 8 cos⁴x - 8 cos²x + 1 <== Right Hand Side