(1) f（x）=α（2cos^2（x/2）+sinx)+b
=2cos^2（x/2）+sinx+b
=cosx+sinx+b-1
=√2sin(x+π/4)+b-1
所以单调增区间为〔2kπ-3/4π,2kπ+1/4π〕
(2)因为a
已知函数f（x）=α（2cos^2 x/2+sinx)+b
(1) f（x）=α（2cos^2（x/2）+sinx)+b
=2cos^2（x/2）+sinx+b
=cosx+sinx+b-1
=√2sin(x+π/4)+b-1
所以单调增区间为〔2kπ-3/4π,2kπ+1/4π〕
(2)因为a