Rút gọn biểu thức \(M = 2{\cos ^2}(\dfrac{\pi }{2} - \dfrac{a}{2}) + \sqrt 2 \sin (\dfrac{\pi }{4} + a) - 1\)
Ta có:
\(M = 2{\cos ^2}(\dfrac{\pi }{2} - \dfrac{a}{2}) + \sqrt 2 \sin (\dfrac{\pi }{4} + a) - 1\)
\( = 2.\dfrac{{1 + \cos \left( {\pi - a} \right)}}{2}\) \( + \sqrt 2 \left( {\sin a\cos \dfrac{\pi }{4} + \cos a\sin \dfrac{\pi }{4}} \right) - 1\)
\( = 1 + \cos \left( {\pi - a} \right)\) \( + \sqrt 2 .\left( {\sin a.\dfrac{1}{{\sqrt 2 }} + \cos a.\dfrac{1}{{\sqrt 2 }}} \right) - 1\)
\( = - \cos a + \sin a + \cos a\) \( = \sin a\)
Chọn A