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[sbabys2]

sin²x ( sin - cosx) + cos²x( cos x - sin x) = sinx + cosx

[chanhquocnghiem]

sin²x ( sin - cosx) + cos²x( cos x - sin x) = sinx + cosx

$\Leftrightarrow (sinx-cosx)(sin^2x-cos^2x)=sinx+cosx$

$\Leftrightarrow sinx+cosx=0$ hoặc $(sinx-cosx)^2=1$

$\Leftrightarrow sinx+cosx=0$ hoặc $sin2x=0$

$\Leftrightarrow x=-\frac{\pi }{4}+k\pi$ ; $x=\frac{k\pi }{2}$ ($k$ thuộc $\mathbb{Z}$)

Edited by chanhquocnghiem, 03-10-2013 - 14:22.