Chứng minh rằng: cos4a=cos^4a+sin^4a-6sin^2a*cos^2a 31/10/2021 Bởi Lyla Chứng minh rằng: cos4a=cos^4a+sin^4a-6sin^2a*cos^2a
Đáp án: $\begin{array}{l}{\cos ^4}a + {\sin ^4}a – 6.{\sin ^2}a.{\cos ^2}a\\ = {\cos ^4}a + 2.{\cos ^2}a.si{n^2}a + {\sin ^4}a – 8{\sin ^2}a.{\cos ^2}a\\ = {\left( {{{\cos }^2}a + {{\sin }^2}a} \right)^2} – 2.4.{\sin ^2}a.{\cos ^2}a\\ = 1 – 2.{\sin ^2}2a\\ = \cos 4a\\Vậy\,\cos 4a = {\cos ^4}a + {\sin ^4}a – 6.{\sin ^2}a.{\cos ^2}a\end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
{\cos ^4}a + {\sin ^4}a – 6.{\sin ^2}a.{\cos ^2}a\\
= {\cos ^4}a + 2.{\cos ^2}a.si{n^2}a + {\sin ^4}a – 8{\sin ^2}a.{\cos ^2}a\\
= {\left( {{{\cos }^2}a + {{\sin }^2}a} \right)^2} – 2.4.{\sin ^2}a.{\cos ^2}a\\
= 1 – 2.{\sin ^2}2a\\
= \cos 4a\\
Vậy\,\cos 4a = {\cos ^4}a + {\sin ^4}a – 6.{\sin ^2}a.{\cos ^2}a
\end{array}$