SOLUTION: Verify that the equation is an identity: sin^4 - cos^4 = 2sin^2 - 1 Also please show the steps if you can. It will be a lot of help since I'm not at all good with Math. Thank

Question 602425: Verify that the equation is an identity:
sin^4 - cos^4 = 2sin^2 - 1
Also please show the steps if you can. It will be a lot of help since I'm not at all good with Math. Thank you! :)
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
sin^4 - cos^4 = 2sin^2 - 1

(sin^2)^2 - (cos^2)^2 = 2sin^2 - 1

(sin^2-cos^2)(sin^2+cos^2) = 2sin^2 - 1

(sin^2-cos^2)(1) = 2sin^2 - 1

sin^2-cos^2 = 2sin^2 - 1

sin^2 - (1 - sin^2) = 2sin^2 - 1

sin^2 - 1 + sin^2 = 2sin^2 - 1

2sin^2 - 1 = 2sin^2 - 1

So this verifies the identity.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Factor the difference of two squares in the LHS:

Note that the right-hand factor in the LHS is just the Pythagorean Identity:

Then, using the Pythagorean identity again in the form , substitute:

Combine terms in the LHS:

John

My calculator said it, I believe it, that settles it

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