SOLUTION: Prove: sin x + sin 3x + sin 5x = (sin^2 3x)/ sin x

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Question 578146: Prove:
sin x + sin 3x + sin 5x = (sin^2 3x)/ sin x
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sin(x) + sin(3x) + sin(5x) ≟ sin%5E2%283x%29%2Fsin%28x%29

sin(3x-2x) + sin(3x) + sin(3x+2x)  

[sin(3x)cos(2x) - cos(3x)sin(2x)] + sin(3x) + [sin(3x)cos(2x) + cos(3x)sin(2x)] 

sin(3x)cos(2x) - cos(3x)sin(2x) + sin(3x) + sin(3x)cos(2x) + cos(3x)sin(2x) 

sin(3x)cos(2x) + sin(3x) + sin(3x)cos(2x)

2sin(3x)cos(2x) + sin(3x)

sin(3x)[2cos(2x) + 1]

sin(3x)[2(2cosē(x)-1) + 1]

sin(3x)[4cosē(x)- 2 + 1]

sin(3x)[4cosē(x)- 1]

sin(3x)[2cosē(x) + 2cosē(x) - 1]

sin(3x)[2cosē(x) + (2cosē(x) - 1)]

sin(3x)[2cosē(x) + cos(2x)]

sin(3x)[2cosē(x) + cos(2x)]%28sin%28x%29%2Fsin%28x%29%29

sin(3x)%28+++%28+2sin%28x%29cos%5E2%28x%29+%2B+cos%282x%29sin%28x%29+%29+++%2Fsin%28x%29+%29++

sin(3x)

sin(3x)+++%28%28+sin%282x%29cos%28x%29+%2B+cos%282x%29sin%28x%29+%29+++%2Fsin%28x%29%29+++

sin(3x)+++%28%28+sin%282x%2Bx%29+%29+++%2Fsin%28x%29+++%29

sin(3x)%28+++%28+sin%283x%29+%29+++%2Fsin%28x%29+++%29

sin%5E2%283x%29%2Fsin%28x%29

Edwin