Find all the solutions of \sin^5 x+\cos^3 x=1

sweetrainyday8s2

sweetrainyday8s2

Answered question

2022-02-28

Find all the solutions of
sin5x+cos3x=1

Answer & Explanation

copausc20

copausc20

Beginner2022-03-01Added 8 answers

sin5xsin2x, cos3xcos2x, and sin2x+cos2x=1, so sin5x+cos3x can be equal to1 if and only if
sin5x=sin2x
and
cos3x=cos2x
, i.e.
sin2x(1sin3x)=0
and
cos2x(1cosx)=0
The first equation has solution: x=kπ or x=π2+2mπ, k, m integers.
The second equation has solution: x=2nπ or x=π2+pπ, n,p integers.
Therefore the solution is either: x=kπ and x=2nπ, or equivalently, x=2nπ for some integer n, or

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