几道三角函数的问题…

1.
解:
y=3sin(x+20°)+5sin(x+80°）

=3sin(x+20°)+5sin(x+20°+60°）

=3sin(x+20°)+5*[sin(x+20°)*cos60°+cos(x+20°)*sin60°]

=3sin(x+20°)+2.5sin(x+20°)+2.5√3*cos(x+20°)

=5.5sin(x+20°)+2.5√3*cos(x+20°)

=5.5*[sin(x+20°)+(5√3/11)*cos(x+20°)]

=5.5*[sin(x+20°)+tana*cos(x+20°)]

=5.5*[sin(x+20°)*cosa+cos(x+20°)*sina]/cosa

=7sin(x+a+20°)

由于sin(x+a+20°)属于[-1,1]
则:当sin(x+a+20°)=1时,
y=3sin(x+20)+5sin(x+80)
取最大值为7

2.由sina+sinb+sinc=0
得:sina+sinb=-sinc
则:(sina+sinb)^2=(sinc)^2 ---①

由cosa+cosb+cosc=0
得:cosa+cosb=-cosc
则:(cosa+cosb)^2=(cosc)^2 ---②

①+②,得:

(sina)^2+(cosa)^2+(sinb)^2+(cosb)^2+2sinsinb+2cosacosb
= (sinc)^2+(cosc)^2

1+1+2cos(a-b)=1

则:cos(a-b)=-1/2

3.
由和差化积公式,得:
sinx+siny
=2sin[(x+y)/2]cos[(x-y)/2]
=2sin(1/2)cos[(x-y)/2]
由于0<