sin(x60°)sin(x-60°)

原式=sin（x+60°）-3cos[180°-（x+60°）]+2sin（x-60°）=sin（x+60°）+3cos（x+60°）+2sin（x-60°）=2sin（x+60°+60°）+2sin（x-60°）=2sin（x-60°+1

根据公式sin（a-b）=sinacosb-cosasinb所以原式=sin(x+105-x+15）=sin120°=√3/2

sin²60°=(根号3/2)^2=3/4cos²60°=(1/2)^2=1/4根号2cos45°=根号2*根号2/2=1sin²60°+cos²60°-根号2cos45°=1-1=0

sin(x+120°）+sin（x+240°）=sinx*cos(120)+cosx*sin(120)+sinx*cos(240)+cosx*sin(240)=-0.5sinx+二分之根号三cosx-0.5sinx-二分之根号三cosx=-

sin方10°+sin方20°+sin方30°+sin方40°+sin方50°+sin方60°+sin方70°+sin方80°+sin方90°=sin²10+sin²80+sin²20+sin²70+

f(x)=2cosxsin(x+60°)-√3sin²x+sinxcosx=2cosx(sinxcos60º+cosxsin60º)-√3sin²x+sinxcosx=sinxcosx+√3cos&#

首先要熟悉三角函数变化：sinx+cosx=√2sin(x+45°),它的取值范围是[-√2,√2]而60°=Pi/3

sin²1°+sin²2°+sin²3°...+sin²45°+sin²46°...+sin²89°＝sin^2(90-89)+sin^2(90-88)+...sin^2(90-4

sin(π/2-x)=cosx原式=sin^21°+……+sin^244°+1/2+cos^244°+……+cos^21°=44+1/2=89/2

原式=cos[(x-25)-(65-x)]=cos(2x-90)=sin2x

cos(180°+x)*sin(x+360°)/[sin(-x-180°)*cos(-180°-x)]=-cosx×sinx/[-sin(180°+x)][cos(180°+x)]=-cosx×sinx/sinx(-cosx)=1

套公式啊,sin(10°+x)cos(50°-x)+sin(50°-x)cos(10°+x)=sin(10°+x+50°-x)=sin60°=√3/2.再问：诶……那cos呢……再答：sin(A+B)=sinAcosB+cosAsinB。s

cos(33°-x)sin(63°-x)-cos(x+57°)sin(27°+x)=cos[90°-(x+57°)]sin[90°-(x+27°]-cos(x+57°)sin(x+27°)=sin(x+57°)cos(x+27°)-cos(

这个用三角函数两角和公式和倍角公式不是可以轻松化简嘛!cos(2x+60°)+(sinx)^2=cos60°cos2x-sin60°sin2x+(sinx)^2=1/2[1-2(sinx)^2]-√3/2×sin2x+(sinx)^2=1/

表示sin60°的平方sin²60°=(√3/2)²=3/4

1/3

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°）+52sin

∵1/sin（120°－x）＋1/sin（120°＋x）＝4√3/3,∴3［sin（120°＋x）＋sin（120°－x）］＝4√3sin（120°＋x）sin（120°－x）,∴6sin120°cosx＝2√3（cos2x－cos240°

tga=5√3/11,0

y=sin(x/2)+sin(60-x/2)=2sin[(x/2+60-x/2)/2]cos[[x/2-(60-x/2)]/2]=2sin30cos(x/2-30)=cos(x/2-30)最大值1