Eduprobe
Question:
Prove the following: cos4x = 1 - 8sin²xcos²x
Solution:
cos4x = 2cos²2x - 1 = 2(2cos²x - 1)² - 1 = 2(4cos⁴x - 4cos²x + 1) - 1 = 8cos⁴x - 8cos²x + 1 = 8cos²x(cos²x - 1) + 1 = 1 - 8cos²xsin²x = 1 - 8sin²xcos²x Hence proved
cos4x = 2cos²2x - 1 = 2(2cos²x - 1)² - 1 = 2(4cos⁴x - 4cos²x + 1) - 1 = 8cos⁴x - 8cos²x + 1 = 8cos²x(cos²x - 1) + 1 = 1 - 8cos²xsin²x = 1 - 8sin²xcos²x Hence proved