Solving a Trigonometric Equation with Identities

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To solve the equation sin x + sin 3x + sin 2x = 1 + cos 2x + cos x, trigonometric identities are essential. The identities used include sin(a + b) and the Pythagorean identity cos²x + sin²x = 1. The solution involves combining terms using the identity sin x + sin y = 2 sin((x+y)/2) cos((x-y)/2) and simplifying cos 2x to 2 cos²(x) - 1. By applying these identities, the problem can be effectively solved. The general solution for x in radians can then be derived from the simplified equation.
Johnny Leong
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How to solve: sin x + sin 3x + sin 2x = 1 + cos 2x + cos x, give general solution in radians for x.
How to get start?
Anyone could help me, please?
 
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You will need the following identities:
\cos^{2}x+\sin^{2}x=1,\cos^{2}x-\sin^{2}x=\cos2x
\sin(a+b)=\sin(a)\cos(b)+\sin(b)\cos(a)
 
I have solved the problem. I have used the identities:
sin x + sin y = 2 sin (x+y)/2 cos(x-y)/2 and cos 2x = 2 cos^2 (x) - 1.
With these two identities, it's easy to solve the problem.
 

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