Solve: cos x = -cos 2x - sin 2x + sin x +1, (for x ∈ [-180, 180]

Proving identities and solving trigonometric Identites
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cos(x)=-1+2sin2(x)-2sin(x)cos(x)+sin(x)+1,

cos(x)=2sin2(x)-2sin(x)cos(x)+sin(x),

0=2sin2(x)-2sin(x)cos(x)+sin(x)-cos(x),

0=sin(x)(2sin(x)+1)-cos(x)(2sin(x)+1)=(sin(x)-cos(x))(2sin(x)+1).

Therefore, sin(x)=cos(x)⇒x=π/4 or sin(x)=-½, x=-π/6. That is, x=45° or -30°.

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