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 acos dfrac{pi }{4} + cos asin 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