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- Homework Statement
- Given the equation $$\sin(2x)+2\sin(x)+2\cos(x) = 0$$ find an equivalent equation on the form ##A+\sin(kx + v)=0## (i.e find the values of the parameters A, k and v).

- Relevant Equations
- $$\sin(2x) = 2\sin(x)\cos(x)$$ $$2\sin(x)+2\cos(x) = 2\sqrt{2}\sin(x + \pi/4)$$

Rewrite the given equation, attempt 1:

##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0##

##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0##

##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here.

Attempt 2:

##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0##

##\sin(x)\cos(x) + \sqrt{2}\sin(x + \pi/4) = 0##, nope, don't know how continue.

I know I can rewrite ##\cos(x)## as ##\sin(\pi/2 - x)##, but I don't see how it should help.

##2\sin(x)\cos(x) + 2\sin(x) + 2\cos(x) = 0##

##\sin(x)\cos(x) + \sin(x) + \cos(x) = 0##

##\sin(x)(\cos(x) + 1) + \cos(x) = 0##, naaah, can't get any relevant out from here.

Attempt 2:

##2\sin(x)\cos(x) + 2\sqrt{2}*\sin(x + \pi/4) = 0##

##\sin(x)\cos(x) + \sqrt{2}\sin(x + \pi/4) = 0##, nope, don't know how continue.

I know I can rewrite ##\cos(x)## as ##\sin(\pi/2 - x)##, but I don't see how it should help.

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