## sara1234 3 years ago Helpp

1. sara1234

@jim_thompson5910 @Nameless

2. jim_thompson5910

sin(3x) = sin(2x + x) sin(3x) = sin(2x)cos(x) + cos(2x)sin(x) sin(3x) = sin(x+x)cos(x) + cos(x+x)sin(x) sin(3x) = [sin(x)cos(x) + cos(x)sin(x)]cos(x) + [cos(x)cos(x) - sin(x)sin(x)]sin(x) sin(3x) = [2cos(x)sin(x)]cos(x) + [cos^2(x) - sin^2(x)]sin(x) sin(3x) = 2cos^2(x)sin(x) + cos^2(x)sin(x) - sin^3(x) Do the same to find cos(3x)

3. jim_thompson5910

I'm using the identities sin(x+y) = sin(x)cos(y) + cos(x)sin(y) cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

4. jim_thompson5910

sry i should have gone further sin(3x) = 3cos^2(x)sin(x) - sin^3(x)

5. sara1234

im confused can you tell me what the answer is so i can check if i got it right?

6. jim_thompson5910

hold on one sec

7. jim_thompson5910

checking the answer, but the second one doesn't seem right, but one sec

8. sara1234

ok thank you

9. jim_thompson5910

well using a graphing calculator, I was able to eliminate choices A through C so that leaves D