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)=1/2
a∈(-π/2,0)
a+π/4(-π/4,π/4)
所以a+π/4=π/6 x=-π/12
2）x∈(π/2,π) 则x/2 ∈(π/4,π/2) 故cos(x/2)>0 cosx