SOLUTION: Verify the following identity: Sin^4x + 2sin^2xcos^2x + cos^4x = 1

Question 623872: Verify the following identity:
Sin^4x + 2sin^2xcos^2x + cos^4x = 1
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

I'm sure there are other ways to do this but probably the easiest is to recognize that the left side is a perfect square trinomial. It fits the pattern of:

with the "a" being and the "b" being . Once we recognize this, the rest is easy. Factoring the left side according to the pattern we get"

We should know well that = 1, so this becomes:

which simplifies to:

And we're finished!!
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