# Thread: Help on a trig problem

1. ## Help on a trig problem

Sin(x)+sin(2x)+sin(x)*Cos(2x)+sin(2x)*cos(x)=0
Solve for all angles x.

Hello, i was hoping someone could help me with this problem. I am not sure if I use the double angles for sin(2x) and cos(2x). If i do, I am not really sure what to do after that. If someone could help me along with at least the first few steps i would be very appreciative.

Thank you

2. $\displaystyle \sin(x)+\sin(2x)+\sin(x)\cos(2x)+\sin(2x)\cos(x)=0$

$\displaystyle \sin(x)+2\sin(x)\cos(x)+\sin(x)(1-2\sin^2x)+2\sin(x)\cos^2(x)=0$

$\displaystyle \sin(x)+2\sin(x)\cos(x)+\sin(x)-2\sin^3x+2\sin(x)\cos^2(x)=0$

$\displaystyle 2\sin(x)+2\sin(x)\cos(x)-2\sin^3(x)+2\sin(x)\cos^2(x)=0$

$\displaystyle \sin(x)+\sin(x)\cos(x)-\sin^3(x)+\sin(x)\cos^2(x)=0$

$\displaystyle \sin(x)(1+\cos(x)-\sin^2(x)+\cos^2(x))=0$

$\displaystyle \sin(x)(1+\cos(x)-\sin^2(x)+\cos^2(x))=0$

$\displaystyle \sin(x)(1+\cos(x)-(1-\cos^2(x))+\cos^2(x))=0$

$\displaystyle \sin(x)(1+\cos(x)-1+\cos^2(x)+\cos^2(x))=0$

$\displaystyle \sin(x)(\cos(x)+\cos^2(x)+\cos^2(x))=0$

$\displaystyle \sin(x)(\cos(x)+2\cos^2(x))=0$

Can you finish it from here?

3. Yes i think i got it from here. Thank you for your time.