SOLUTION: verify trigonometric equation as identity sin^4x-cos^4x=2sin^2x-1

Algebra ->  Trigonometry-basics -> SOLUTION: verify trigonometric equation as identity sin^4x-cos^4x=2sin^2x-1      Log On


   

Question 561913: verify trigonometric equation as identity
sin^4x-cos^4x=2sin^2x-1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin%5E4%28x%29 - cos%5E4%28x%29 ≟ 2sin%5E2%28x%29 - 1

Factor the left side:

[sin%5E2%28x%29 - cos%5E2%28x%29][sin%5E2%28x%29 + cos%5E2%28x%29]

Use the identity sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1 to replace the 2nd factor by 1

[sin%5E2%28x%29 - cos%5E2%28x%29][1]

sin%5E2%28x%29 - cos%5E2%28x%29

Use the identity cos%5E2%28theta%29=1-sin%5E2%28theta%29 to replace the 2nd term

sin%5E2%28x%29 - (1-sin%5E2%28x%29)

sin%5E2%28x%29 - 1 + sin%5E2%28x%29

Combine the sinē terms:

2sin%5E2%28x%29 - 1

Edwin