SOLUTION: Rewrite "sin 3x" with only sin x and cos x. OPTIONS: 2 sin x cos^2x + cos x 2 sin x cos^2x + sin^3x sin x cos^2x - sin^3x + cos^3x 2 cos^2x sin x + sin x - 2 sin^3x

Algebra ->  Trigonometry-basics -> SOLUTION: Rewrite "sin 3x" with only sin x and cos x. OPTIONS: 2 sin x cos^2x + cos x 2 sin x cos^2x + sin^3x sin x cos^2x - sin^3x + cos^3x 2 cos^2x sin x + sin x - 2 sin^3x      Log On


   

Question 1086857: Rewrite "sin 3x" with only sin x and cos x.


OPTIONS:
2 sin x cos^2x + cos x
2 sin x cos^2x + sin^3x
sin x cos^2x - sin^3x + cos^3x
2 cos^2x sin x + sin x - 2 sin^3x
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

write
sin%283x%29 as sin%28x%2B2x%29
use the formula and expand:
sin%28x%2By%29=sin%28x%29cos%28y%29%2Bcos%28x%29sin%28y%29
sin%28x%2B2x%29=sin%28x%29cos%282x%29%2Bcos%28x%29sin%282x%29..........since cos%282x%29=cos%5E2%28x%29+-+sin%5E2%28x%29 and sin%282x%29=2sin%28x%29cos%28x%29, we have
......since sin%5E2%28x%29=1-cos%5E2%28x%29 we have




sin%28x%2B2x%29=sin%28x%29%282cos%5E2%28x%29+-+1%29%2B2+sin%28x%29+cos%5E2%28x%29.....since cos%5E2%28x%29=1-sin%5E2%28x%29 we have

sin%28x%2B2x%29=2sin%28x%29cos%5E2%28x%29+-+sin%28x%29%2B2+sin%28x%29%281-+sin%5E2%28x%29%29

sin%28x%2B2x%29=2sin%28x%29cos%5E2%28x%29+-+sin%28x%29%2B2+sin%28x%29-+sin%5E3%28x%29

sin%28x%2B2x%29=2cos%5E2%28x%29sin%28x%29%2B+sin%28x%29+-+2sin%5E3%28x%29
so,
sin%283x%29=2cos%5E2%28x%29sin%28x%29%2B+sin%28x%29+-+2sin%5E3%28x%29