Express cos4x as a trig function of x

Question

Using only the double angle identities how to solve for this? im stucked after 2cos^2 (2x) -1

Answer 1

Use the double angle formula twice.

 

cos(4x) = cos[2(2x)] = 2cos²(2x) - 1

 

                             = 2{2cos²x - 1}² - 1

 

                             = 2{4cos⁴x - 4cos²x + 1} - 1

 

                             = 8cos⁴x - 8cos²x + 1