Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \cos \left( {a + \dfrac{\pi }{4}} \right) + \cos \left( {a - \dfrac{\pi }{4}} \right)\\
= 2.\cos \dfrac{{\left( {a + \dfrac{\pi }{4}} \right) + \left( {a - \dfrac{\pi }{4}} \right)}}{2}.\cos \dfrac{{\left( {a + \dfrac{\pi }{4}} \right) - \left( {a - \dfrac{\pi }{4}} \right)}}{2}\\
= 2.\cos \dfrac{{2a}}{2}.\cos \dfrac{{\dfrac{\pi }{2}}}{2}\\
= 2\cos a.\cos \dfrac{\pi }{4}\\
= \sqrt 2 \cos a\\
B = {\sin ^2}x + 2\cos x + 1\\
= \left( {1 - {{\cos }^2}x} \right) + 2\cos x + 1\\
= - {\cos ^2}x + 2\cos x + 2\\
= - \left( {{{\cos }^2}x - 2\cos x + 1} \right) + 3\\
= 3 - {\left( {\cos x - 1} \right)^2} \le 3,\,\,\,\,\forall x\\
\Rightarrow {B_{\max }} = 3 \Leftrightarrow \cos x - 1 = 0 \Leftrightarrow \cos x = 1 \Leftrightarrow x = k2\pi
\end{array}\)
