Toán Tìm gtln-nn của hs y= 4cos^4x +4sin^2x -5 23/09/2021 By Adalynn Tìm gtln-nn của hs y= 4cos^4x +4sin^2x -5
\[\begin{array}{l} y = 4{\cos ^4}x + 4{\sin ^2}x – 5\\ = 4{\cos ^4}x – 4{\cos ^2}x + 4 – 5\\ = 4{\cos ^4}x – 4{\cos ^2}x + 1 – 2\\ = {\left( {2{{\cos }^2}x – 1} \right)^2} – 1 \ge – 1\\ \Rightarrow Min\,y = – 1\,\,\,khi\,\,\,{\cos ^2}x = \frac{1}{2}. \end{array}\] Trả lời
\[\begin{array}{l}
y = 4{\cos ^4}x + 4{\sin ^2}x – 5\\
= 4{\cos ^4}x – 4{\cos ^2}x + 4 – 5\\
= 4{\cos ^4}x – 4{\cos ^2}x + 1 – 2\\
= {\left( {2{{\cos }^2}x – 1} \right)^2} – 1 \ge – 1\\
\Rightarrow Min\,y = – 1\,\,\,khi\,\,\,{\cos ^2}x = \frac{1}{2}.
\end{array}\]