Integral n for \sin^n(x) + \cos^n(x) = 1-\frac{n}{2}\sin^2(x)\cos^2(x) is n=4,6. I

Travis Caldwell

Travis Caldwell

Answered question

2022-04-22

Integral n for sinn(x)+cosn(x)=1n2sin2(x)cos2(x) is n=4,6.
I have proved for n=4,6 it is true, for other integer, I tried to check range of functions on left and right side. This is not as effective, and I failed. Please suggest a method in this.

Answer & Explanation

Patricia Duffy

Patricia Duffy

Beginner2022-04-23Added 16 answers

x=π4 gives
12n21=1n8
and the RHS goes to where LHS goes to 0 a n

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