T TÍNH MỖI CÁI LÀ RA, HAHA (>_<)
y′=x′.tanx+.tan′x=tanx+xcos2x
y″
VT=x^2.y''-2(x^2+y^2)(1+y)
=x^2(\frac{2}{\cos^2x}+\frac{2x.\sin x}{\cos^3x})-2(x^2+x^2.\tan^2x)(1+x.\tan x)
=\frac{2x^2}{\cos^2x}+\frac{2x^3.\sin x}{\cos^3x}-2(x^2+x^3.\tan x + x^2.\tan^2x+x^3.\tan^3x)
=\frac{2x^2}{\cos^2x}+\frac{2x^3.\sin x}{\cos^3x}-2x^2-\frac{2x^3.\sin x}{\cos x}-\frac{2x^2 \sin^2x}{\cos^2x}-\frac{2x^3.\sin^3x}{\cos^3x}
=\frac{2x^2}{\cos^2 x}(1-\sin ^2x)+\frac{2x^3.\sin x}{\cos^3 x}(1-\sin^2x)-2x^2-\frac{2x^3.\sin x}{\cos x}
=2x^2+\frac{2x^3.\sin x}{\cos x}-2x^2-\frac{2x^3.\sin x}{\cos x}=0=VP (đpcm)
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