Вычислить (sin^2(x))/cos(x)-(cos^2(x)/sin(x) если sin(x)-cos(x)=0.5 . Created by dimamityai. algebra-ru

sin(x) если sin(x)-cos(x)=0.5 ...

irkarom

sin²x/cosx - cos²x/sinx=(sin³x-cos³x)/ (sinx cosx)

(sinx-cosx)²=sin²x-2 sinx cosx+ cos²x=1-sin2x =(0,5)²,

sin2x= 0,75 , sinx cosx =1/2sin2x=0,375

sin³x-cos³x=(sinx-cosx)(sin²x+sinx cosx+cos²x)=

=0,5(1+1/2 * sin2x)=0,5 (1+1/2 * 0,75)=0,6875

Исходное выражение равно 0,6875 / 0,375 =1,8(3)

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Verified answer

$\frac{sin^2x}{cosx}-\frac{cos^2x}{sinx} =\frac{sin^2x*sinx-cos^2x*cosx}{cosx*sinx}=\frac{sin^3x-cos^3x}{cosx*sinx}=\\ =\frac{(cosx-sinx)(sin^2x+sinxcosx+cos^2x)}{cosx*sinx}=\frac{(cosx-sinx)(1+sinxcosx)}{cosx*sinx}\\$

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