已知f(x)=sinx+2sin(π/4+x/2)cos(π/4+x/2).(1)若f(a)=√2/2,a∈(-π/2,0),求a的值(2)若sin(x/2)=4/5,x∈(π/2,π),求f(x)的值

问题描述:

已知f(x)=sinx+2sin(π/4+x/2)cos(π/4+x/2).
(1)若f(a)=√2/2,a∈(-π/2,0),求a的值
(2)若sin(x/2)=4/5,x∈(π/2,π),求f(x)的值

1)利用2倍角公式f(x)=sinx+sin[2(π/4+x/2)]=sinx+sin(π/2+x)=sinx+cosx=√2(√2/2sinx+√2/2cosx)=√2(cosπ/4 sinx+sinπ/4 cosx)注意里面是π/4,别看错了=√2sin(x+π/4)f(a)=√2/2即sin(x+π/4)=1/2a∈(-π/2,...