若方程根号3sinx

sinx+√3cosx)+a=2(1/2sinx+√3/2cosx)+a（利用公式sin(π/6)=1/2;cos(π/6)=√3/2）=2(sin(π/6)sinx+cos(π/6)cosx)+a=

sinx+3cosx=1即sin（π3+x）=12又 π＜x＜2π∴4π3＜π3+x＜7π3∴π3+x=13π6解得：x=11π6故答案为：11π6

sin（α+β）=sinαcosβ+cosαsinβ两边同时除以2得到cos60sinx+cosx+sin60=-a/2sin（x+60）=-a/2所以x+pi/3在[pi/3,4pi/3]有解sin

化简一下就可以sinx+√3*cosx+a=02[(1/2)sinx+√3/2*cosx]+a=02sin(x+π/3)+a=0因为上式在[0,π]内有解所以π/3=

若方程sinx+(√3)cosx+2a-1=0在[0,π]上有两个不相等的实数根,求实数a的取值范围sinx+(√3)cosx=1-2a2[(1/2)sinx+(√3/2)cosx]=2[sinxco

sinx+根号3cosx=22(sinx/2+根号3cosx/2)=2sinx/2+根号3cosx/2=1sinxcosπ/3+cosxsinπ/3=1sin(x+π/3)=1所以x+π/3=2kπ+

切点为P0(π/3,√3/2)k=(sinx)'|(x=π/3)=cos(π/3)=(1/2)切线方程P0T:y-(√3/2)=(1/2)(x-π/3)

根号下(sinx-（sinx)^3)dx=根号下(sinx[1-（sinx)^2])dx=根号下(sinx*cos^2x)dx=根号下(sinx)*cosxdx=根号下(sinx)*dsinx=2/3

√3cosx-sinx=0√3cosx=sinxsinx/cosx=√3tanx=√3x=kπ+π/3

=2*(根号3sinx/2+cosx/2)=2(sinx*cos30°+cosxsin30°）=2sin（x+30°)

sinx和cosx是方程2X^2-(根号3+1)x+m=0的两个根则,由韦达定理得：sinx+cosx=(√3+1)/2sinx/(1-COtX)+COSX/(1-tanx)=sinx/(1-cosx

y=2Sin(x+π/3）对称轴是x=π/6+kπ,（k为整数）

y=sin(x/2)＋√3cos(x/2)y=2sin[(x/2)＋π/3]其对称轴是(x/2)＋(π/3)=kπ＋π/2即对称轴是：x=2kπ＋π/3,k∈Z

√3sinx-cosx=2(sinxcosπ/6-cosxsinπ/6)=2sin(x-π/6)

=(sinx)^2+√3sinxcosx=(1-cos2x)/2+√3/2(2sinxcosx)=1/2-1/2cosx+√3/2sin2x=1/2+sin(-π/6)cos2x+cos(-π/6)s

当sinx≤cosx,即-3π/4+2kπ≤x≤π/4+2kπ,k∈Z时,f(x)=1/2(sinx+cosx+sinx-cosx)=sinx当sinx＞cosx,即π/4+2kπ＜x＜5π/4+2k

√3cosx-sinx=12((√3/2)cosx-(1/2)sinx)=12cos(x+π/6)=1cos(x+π/6)=1/2x+π/6=π/3or5π/3x=π/6or3π/24sinx+3co

√3sinx-cosx=sinx+√3cosx两边同时处以2得√3sinx/2-cosx/2=sinx/2+√3cosx/2sinxcos(π/6)-cosxsin(π/6)=sinxcos(π/3)

sinx-根号cosx=2(1/2sinx-根号3/2cosx)=2(cos60shinx-sin60cosx)=2sin(x-60)=根号2.得到sin(x-60)=根号2/2得到x-60=45+3

2√3(1-sin²x)=sinx2√3sin²x+sinx-2√3=0(2sinx-√3)(√3sinx+2)=02sinx-√3=0或√3sinx+2=0sinx=√3/2或s