Toán Lớp 9: rút gọn biểu thức sin^6a+cos^6a+3sin^2acos^2a-sin^2a
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Toán Lớp 9: rút gọn biểu thức sin^6a+cos^6a+3sin^2acos^2a-sin^2a
Comments ( 1 )
{\sin ^6}a + {\cos ^6}a + 3{\sin ^2}a.{\cos ^2}a – {\sin ^2}a\\
= \left( {{{\sin }^2}a + {{\cos }^2}a} \right).\left( {{{\sin }^4}a – {{\sin }^2}a.{{\cos }^2}a + {{\cos }^4}a} \right)\\
+ 3{\sin ^2}a.{\cos ^2}a – {\sin ^2}a\\
= 1.\left[ {{{\left( {{{\sin }^2}a + {{\cos }^2}a} \right)}^2} – 3{{\sin }^2}a.{{\cos }^2}a} \right]\\
+ 3{\sin ^2}a.{\cos ^2}a – {\sin ^2}a\\
= 1 – 3{\sin ^2}a.{\cos ^2}a + 3{\sin ^2}a.{\cos ^2}a – {\sin ^2}a\\
= 1 – {\sin ^2}a\\
= {\cos ^2}a
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