Values of x satisfying \sin x \cdot \cos^3 x >

Gavin Frye

Gavin Frye

Answered question

2022-01-26

Values of x satisfying sinxcos3x>sin3xcosx
My Attempt
sinxcosx(cos2xsin2x)=12sin2xcos2x=14sin4x>0sin4x>0x(0,π)4x(0,4π)
4x(0,π)(2π,3π)x(0,π4)(π2,3π4)
But, my reference gives the solution, x(0,π4)(3π4,π) where am I going wrong with my attempt?

Answer & Explanation

jojoann325

jojoann325

Beginner2022-01-27Added 10 answers

The given solution is wrong; you are correct. At x=7π8(3π4,π) we have that
14sin4x=14sin7π2=14<0
which is a contradiction.

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