Question
Prove that it is an identity: cos (4x)=8cos^4(x)-8cos^2(x)+1
Answers
Reiny
Using the property : cos 2A = 2cos^2 A -1
cos(4x)
= 2cos^2 (2x) - 1 = 2(cos(2x))(cos(2x)) - 1 , using the same property again
= 2(2cos^2 x - 1)^2 - 1
= 2(4cos^4 x - 4cos^2 x + 1) - 1
= 8cos^4 x - 8cos^2 x + 1
= RS
cos(4x)
= 2cos^2 (2x) - 1 = 2(cos(2x))(cos(2x)) - 1 , using the same property again
= 2(2cos^2 x - 1)^2 - 1
= 2(4cos^4 x - 4cos^2 x + 1) - 1
= 8cos^4 x - 8cos^2 x + 1
= RS