SOLUTION: 84. confirm the identity cos^4x-sin^4x=cos2x
Algebra.Com
Question 174478: 84. confirm the identity cos^4x-sin^4x=cos2x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
cos^4x-sin^4x=cos(2x)... Start with the given equation.
(cos^2(x))^2-(sin^2(x))^2=cos(2x) ... Factor cos^4x into (cos^2(x))^2. Factor sin^4x into (sin^2(x))^2.
((1+cos(2x))/2)^2-((1-cos(2x))/2)^2=cos(2x) ... Use the power reducing identities
((1+cos(2x))/2+(1-cos(2x))/2)((1+cos(2x))/2-(1-cos(2x))/2)=cos(2x) ... Factor the left side using the difference of squares formula
(2/2)((2cos(2x))/2)=cos(2x) ... Combine the fractions and like terms.
cos(2x)=cos(2x) ... Reduce. So this verifies the identity
RELATED QUESTIONS
Prove the following identity:
cos 4x = cos^4x - 6cos^2xsin^2s +... (answered by venugopalramana)
Verify the identity:
{{{Sin(x)(1-2*Cos^2x+ Cos^4x) =... (answered by Edwin McCravy)
Verify the solution and show your work:
cos^4X - sin^4X =... (answered by robertb)
Verify the trig identity: sin^4(x)+cos^4 (x)=3/4 + 1/4 cos(4x). (answered by jsmallt9)
Verify the following identity:
Sin^4x + 2sin^2xcos^2x + cos^4x =... (answered by jsmallt9)
Prove the identity:... (answered by Alan3354)
Consider the following equation:
cos2x = cos^4x - sin^4x
Verify the statement for... (answered by MathLover1)
Please help me with the following question.
Prove this identity:... (answered by Alan3354,josgarithmetic,MathTherapy)
simplify the expression: cscx(tan(-x))
simplify the expression: cotxcos(3.14/2-x)... (answered by kev82,funmath)