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\(B=\dfrac{1-4\sin^2x\cdot\cos^2x}{\sin^2x+2\sin x\cdot\cos x+\cos^2}+2\sin x\cdot\cos x\\ B=\dfrac{1-4\sin^2x\cdot\cos^2x}{2\sin x\cdot\cos x}+2\sin x\cdot\cos x\\ B=\dfrac{1-4\sin^2x\cdot\cos^2x+4\sin^2x\cdot\cos^2x}{2\sin x\cdot\cos x}=\dfrac{1}{2\sin x\cdot\cos x}\)
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\(A=s\left(x\right)cs\left(x\right)+\frac{\left(s^3\left(x\right)+cs^3\left(x\right)\right)}{cs\left(x\right)\left(1+t\left(x\right)\right)}=s\left(x\right)cs\left(x\right)+\left(\frac{\left(s\left(x\right)+cs\left(x\right)\right)\left(1-s\left(x\right)cs\left(x\right)\right)}{\left(s\left(x\right)+cs\left(x\right)\right)}\right)\)
\(=1\) vì \(s\left(x\right)+cs\left(x\right)\ne0,\forall0< =x< =\frac{\pi}{2}\)
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\(=\frac{\left(sina+cosa\right)\left(sina-cosa\right)}{sin^2a+cos^2a+2sina\cdot cosa}\) =\(\frac{\left(sina+cosa\right)\left(sina-cosa\right)}{\left(sina+cosa\right)^2}=\frac{sina-cosa}{sina+cosa}=\frac{tana-1}{\tan a+1}\)
\(A=\frac{2.\left(cosx+1\right)-sin^2x}{sinx.\left(cosx+1\right)}=\frac{2.cosx+2-sin^2x}{sinx.\left(cosx+1\right)}=\frac{2.cosx+1+cos^2x}{sinx.\left(cosx+1\right)}=\frac{\left(cosx+1\right)^2}{sinx.\left(cosx+1\right)}=\frac{cosx+1}{sinx}\)