How to prove that sin4(x) is evenFunction is even when f(x)=f(-x), so my aim is to prove that sin4(x) is even. So I could write it like sin4(−x) which, in turn, is (−sin⁡(x))×(−sin⁡(x))×(−sin⁡(x))×(−sin⁡(x)) and equal to the one with positive x. Is that enough prove or I should expose it in some other way?

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legaldaj1dn · Accepted Answer

note that we havef(x)=(sin⁡(x))4then we getf(−x)=(sin⁡(−x))4=(−sin⁡(x))4=(sin⁡(x))4=f(x)

szkliwiakinrd · Accepted Answer

Yes, this is a good way to do it. We know that sin⁡(x) is odd, meaning that sin⁡(−x)=−sin⁡(x). In a more condensed form:sin4(−x)=(sin⁡(−x))4=(−sin⁡(x))4=(−1)4(sin⁡(x))4then we know (−1)4=1

How to prove that \(\displaystyle{{\sin}^{{4}}{\left({x}\right)}}\) is even Function

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