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Prove that `cos^4A - sin^4A +1 = 2cos^2A`
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High School Teacher
First, group the first two terms and factor it.
Then, apply the Pythagorean identity which is `cos^2theta + sin^2theta=1` .
`cos^2A-sin^2A + 1=2cos^2A`
Then, group the second and last term at the left side of the equation.
To simplify the expression inside the parenthesis, apply the Pythagorean identity again.
Since left side simplifies to `2cos^2A` which is the same term with the right side, hence it proves that the given equation is an identity.
Posted by mjripalda on April 9, 2013 at 11:17 AM (Answer #1)
Posted by oldnick on April 10, 2013 at 12:09 AM (Answer #2)
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