(1+tana).sin^3a + ( 1+tana).cos^3a = sina+cosa 09/08/2021 Bởi Elliana (1+tana).sin^3a + ( 1+tana).cos^3a = sina+cosa
$\begin{array}{l} \left( {1 + \tan a} \right){\cos ^3}a + \left( {1 + \cot a} \right){\sin ^3}a\\ = \left( {1 + \dfrac{{\sin a}}{{\cos a}}} \right){\cos ^3}a + \left( {1 + \dfrac{{\cos a}}{{\sin a}}} \right){\sin ^3}a\\ = {\cos ^3}a + {\sin ^3}a + \sin a.{\cos ^2}a + {\sin ^2}a\cos a\\ = \left( {{{\cos }^3}a + \sin a.{{\cos }^2}a} \right) + \left( {{{\sin }^3}a + {{\sin }^2}a\cos a} \right)\\ = {\cos ^2}a\left( {\sin a + \cos a} \right) + {\sin ^2}a\left( {\sin a + \cos a} \right)\\ = \left( {\sin a + \cos a} \right)\left( {{{\sin }^2}a + {{\cos }^2}a} \right) = \sin a + \cos a \end{array}$ Bình luận
$\begin{array}{l} \left( {1 + \tan a} \right){\cos ^3}a + \left( {1 + \cot a} \right){\sin ^3}a\\ = \left( {1 + \dfrac{{\sin a}}{{\cos a}}} \right){\cos ^3}a + \left( {1 + \dfrac{{\cos a}}{{\sin a}}} \right){\sin ^3}a\\ = {\cos ^3}a + {\sin ^3}a + \sin a.{\cos ^2}a + {\sin ^2}a\cos a\\ = \left( {{{\cos }^3}a + \sin a.{{\cos }^2}a} \right) + \left( {{{\sin }^3}a + {{\sin }^2}a\cos a} \right)\\ = {\cos ^2}a\left( {\sin a + \cos a} \right) + {\sin ^2}a\left( {\sin a + \cos a} \right)\\ = \left( {\sin a + \cos a} \right)\left( {{{\sin }^2}a + {{\cos }^2}a} \right) = \sin a + \cos a \end{array}$