SOLUTION: Prove: Cos^4(x) - Sin^4(x) = 1 - 2Sin^2(x) Thank you

Algebra.Com
Question 927209: Prove:
Cos^4(x) - Sin^4(x) = 1 - 2Sin^2(x)
Thank you

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Prove:
Cos^4(x) - Sin^4(x) = 1 - 2Sin^2(x)
------
(cos^2)^2 - (sin^2)^2 = 1 - 2sin^2
-------
(1-sin^2)^2 - (sin^2)^2 + 2sin^2 = 1
------
1 - 2sin^2 + sin^4 -sin^4 + 2sin^2 = 1
-----
1 = 1
------
Cheers,
Stan H.
--------------

RELATED QUESTIONS

Prove that... (answered by MathLover1)
Please help prove identity: {{{2sin(2x)cos(2x)=4cos(x)(sin(x)-2(sin(x))^3)}}} thank... (answered by eggsarecool)
Prove the identity: 2Sin X • Cos X ÷ (Sin X + Cos X)^2 - 1 = 1 (answered by Shai)
Verify: sin^4 (x)-cos^4... (answered by tommyt3rd)
Verify identity.... (answered by MathLover1)
please help prove:... (answered by Alan3354)
Prove that sin x+ cos x =sqrt(2)sin(x+pi/4) Please show the steps in detail, thank... (answered by jim_thompson5910)
Good evening, I'm stuck on this question, sin(x)cos(x)cos(2x)=(sin(4x))/4 I've been... (answered by jsmallt9)
Prove the identity: {{{sin(2x)/(2sin(x))=cos^2(x/2) -... (answered by Edwin McCravy)