Analytically solving \frac{1}{\sin 2x}+\frac{1}{\sin 3x}=\frac{1}{\sin x}

Harold Kessler

Harold Kessler

Answered question

2022-01-16

Analytically solving 1sin2x+1sin3x=1sinx

Answer & Explanation

macalpinee3

macalpinee3

Beginner2022-01-17Added 29 answers

Hint:
Remember sinx0cosx±1
From
(2c)3(2c)22(2c)+1=0
Replace 2c with y+1y where y=eix to find
(y+1y)3(y+1y)22(y+1y)+1
=y3+1y3+3(y+1y)y21y222(y+1y)+1
=y71y3(y1)

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