Find an identity for cos(4t) in terms of cos(t)cos⁡(t).

Question

Any identity please? I'm not sure which one fits this problem.

Answer 1

cos(4t) = cos[2(2t)] = 2cos²(2t) - 1

 

                              = 2{2cos²t - 1}² - 1

 

                              = 2{4cos⁴t - 4cos²t + 1} - 1

 

                              = 8cos⁴t - 8cos²t + 1

 

 

Answer 2

Invent one!  Expand cos (2t+2t).