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Winigefx 2022-06-24 Answered
trigonometry equation - sin 3 ( x ) + sin 3 ( 2 x ) + sin 3 ( 3 x ) = ( sin ( x ) + sin ( 2 x ) + sin ( 3 x ) ) 3
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Answers (1)

Lilliana Burton
Answered 2022-06-25 Author has 19 answers
Let sin x = a, sin 2 x = b, and sin 3 x = c
Expand out
( a + b + c ) 3
Then subtract a 3 , b 3 and c 3 , which yields
3 a 2 b + 3 a 2 c + 3 a b 2 + 6 a b c + 3 a c 2 + 3 b 2 c + 3 b c 2 = 0
The long expression can be factored nicely into :
3(a+b)(b+c)(a+c), which equal to 0.
The factor 3 makes no difference, so solve for:
sin ( x ) + sin ( 2 x ) = 0,
sin ( 2 x ) + sin ( 3 x ) = 0, and
sin ( x ) + sin ( 3 x ) = 0.
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