SOLUTION: how to verify the identity of problem cos^4(x)-sin^4(x)=2cos^2(x)-1

Question 410613: how to verify the identity of problem
cos^4(x)-sin^4(x)=2cos^2(x)-1
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
cos^4(x)-sin^4(x)=2cos^2(x)-1
..
cos^4-sin^4=2cos^2-1
starting with left-hand side
using difference of squares
(cos^2+sin^2)((cos^2-sin^2)
=(1)(cos^2-sin^2)
=cos^2-(1-cos^2)
=cos^2-1+cos^2
=2cos^2-1
confirmed: Left-hand side=Right-hand side
RELATED QUESTIONS
verify the identity... (answered by Edwin McCravy)

how to verify the identity of problem... (answered by lwsshak3)

Verify the trig identity: sin^4(x)+cos^4 (x)=3/4 + 1/4 cos(4x). (answered by jsmallt9)

Verify the identity: (cos x-sin... (answered by robertb)

How to verify the identity of sin x / 1 - cos... (answered by fcabanski,Alan3354)

Verify identity.... (answered by MathLover1)

Please verify the following identity: cos^4 x + sin^2 x = cos^2 x + sin^4... (answered by Tatiana_Stebko)

Verify that each equation is an identity (2cos^2 (X/2)) (tan X) = tan X + sin X... (answered by lwsshak3)