Buktikan identitas trigonometri ini! cos 3θ = (sin θ + cos θ)(1 - 2 sin 2θ) + sin 3θ

[tex]\cos{3x}=\cos{2x}\cos{x}-\sin{2x}\sin{x}\\=(\cos^2{x}-\sin^2{x})\cos{x}-2\sin^2{x}\cos{x}\\=\cos^3{x}-\cos{x}(1-\cos^2{x})-2\cos{x}(1-\cos^2{x})\\=4\cos^3{x}-3\cos{x}\\=4\cos^3{x}-4\cos{x}+\cos{x}+\sin{x}-\sin{x}+\sin^3{x}-\sin^3{x}\\=-4\cos{x}(1-\cos^2{x})+\cos{x}+\sin{x}-\sin{x}(1-\sin^2{x})+\sin^3{x}\\=-4\cos{x}\sin^2{x}+\cos{x}+\sin{x}-\cos^2{x}\sin{x}-\sin^3{x}\\=-4\cos{x}\sin^2{x}+\cos{x}+\sin{x}-\cos^2{x}\sin{x}-\sin^3{x}\\=\cos{x}+\sin{x}-4\cos{x}\sin^2{x}-4\cos^2{x}\sin{x}+2\cos^2{x}\sin{x}\\+\cos^2{x}\sin{x}-\sin^3{x}\\=\cos{x}+\sin{x}-4\cos{x}\sin{x}(\cos{x}+\sin{x})+(2\sin{x}\cos{x})\cos{x}\\+\sin{x}(\cos^2{x}-\sin^2{x})\\=(\cos{x}+\sin{x})(1-4\cos{x}\sin{x})+\sin{2x}\cos{x}+\sin{x}\cos{2x}\\=(\cos{x}+\sin{x})(1-2\sin{2x})+\sin{3x}[/tex]