\( VT = {\tan ^2}x - {\sin ^2}x\\ = {\left( {\dfrac{{{\mathop{\rm sinx}\nolimits} }}{{\cos x}}} \right)^2} - {\sin ^2}x\\ = \dfrac{{{{\sin }^2}x}}{{{{\cos }^2}x}} - \dfrac{{\left( {{{\sin }^2}x} \right)\left( {{{\cos }^2}x} \right)}}{{{{\cos }^2}x}}\\ = \dfrac{{{{\sin }^2}x - \left( {{{\sin }^2}x} \right)\left( {1 - {{\sin }^2}x} \right)}}{{{{\cos }^2}x}}\\ = \dfrac{{{{\sin }^2}x - {{\sin }^2}x + {{\sin }^4}x}}{{{{\cos }^2}x}} = \dfrac{{{{\sin }^4}x}}{{{{\cos }^2}x}} \\= \dfrac{{{{\sin }^2}x}}{{{{\cos }^2}x}}.{\sin ^2}x = {\tan ^2}x.{\sin ^2}x = VP\left( {đpcm} \right) \)
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