How do you prove that # 2cos^4x + (2-2cos^2x)cos^2x = cos2x + 1 #?
1 Answer
Feb 28, 2016
If you simplify the left hand side of the equation it is simply
It then becomes the double angle identity for
#2cos^2x = cos2x + 1#
Explanation:
The double angle identity is a special case of the compound angle formula.
#cos(a+b) = cos(a)cos(b) - sin(a)sin(b)#
So letting
#cos(2x) = cos(x+x)#
#= cos(x)cos(x) - sin(x)sin(x)#
#= cos^2(x) - sin^2(x)#
#= cos^2(x) - [1 - cos^2(x)]#
#= 2cos^2(x) - 1#
