Question

哪位大神能写出第十一题的详细过程

Answer 1

x∈(0，π)，则sinx>0
sinx+cosx=1/5
cosx=1/5 -sinx
sin²x+cos²x=1
sin²x+(1/5 -sinx)²=1
25sin²x -5sinx-12=0
(5sinx+3)(5sinx-4)=0
sinx=-3/5(舍去)或sinx=4/5
sin²(x/2 +π/12)+√3sin(x/2 +π/12)cos(x/2 +π/12) -½
=½[1-cos(x+ π/6)]+(√3/2)sin(x+ π/6) -½
=(√3/2)sin(x+ π/6)-½cos(x+ π/6)
=sin(x+ π/6)cos(π/6)-cos(x+ π/6)sin(π/6)
=sin(x+ π/6- π/6)
=sinx
=4/5
选A