Advanced Math/trig

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Question
how do i prove a trig identies with sin(3x)+3sin(x)- 4sin^3(x). I just dont understand how to simlify sin(3x)

Answer
sin(3x) + 3sin(x) - 4sin(x)^3

sin(2x + x) + 3sin(x) - 4sin(x)^3

(sin(2x)cos(x) + sin(x)cos(2x)) + 3sin(x) - 4sin(x)^3

(2sin(x)cos(x)^2 + sin(x)(1 - 2sin(x)^2)) + 3sin(x) - 4sin(x)^3

(2sin(x)cos(x)^2 + sin(x) - 2sin(x)^3) + 3sin(x) - 4sin(x)^3

2sin(x)cos(x)^2 + sin(x) - 2sin(x)^3 + 3sin(x) - 4sin(x)^3

2sin(x)(1 - sin(x)^2) + 4sin(x) - 6sin(x)^3

2sin(x) - 2sin(x)^3 + 4sin(x) - 6sin(x)^3

6sin(x) - 8sin(x)^3

ANS : -8sin(x)^3 + 6sin(x)

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I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

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