9.已知函數(shù)f(x)=sinx*2+2√3sinxcos+3cos*2x (2)已知f(a)=3,且a∈(0,π),求a的值
f(x)=sin^x+2√3sinxcosx+3cos^2x
=(sin^2x+ cos^2x) +2cos^2x +√3sin2x=√3sin2x + cos2x +2
=2sin(2x+π/6)+2
f(a)=2sin(2a+π/6)+2=3
sin(2a+π/6)=1/2
2a+π/6=π/6 或者 2a+π/6= 5π/6
a=0 （舍）或者a=π/3
10.已知函數(shù)f(x)=sin(π/2+x)cos-sinxcos(π-x)(2)在△ABC中,已知A為銳角,f(A)=1,BC=2,B=π/3,求AC邊的長
f(x)=sin(π/2+x)cosx - sinxcos(π-x）= cosx cosx - sinx (- cosx)
= cos^x + sinx cosx= ( 1+ cos2x)/2 + (1/2)*sin2x
=√2/2 (√2/2 cos2x+ √2/2sin2x) + 1/2
= √2/2 sin(2x+π/4) + 1/2
由于 f(A)= √2/2 SIN(2A +π/4)+1/2= 1
SIN(2A + π/4)=√2/2
0