a属于（π/2,π）,1/sina+1/cosa=2根号2,则sin(2a+π/3)=______
(sina+cosa)/sinacosa=2√2sina+cosa=2√2sinacosa平方sin²a+cos²a+2sinacosa=8(sinacosa)²1+sin2a=8(1/2*sin2x)²=2sin²2a(2sin2a+1)(sin2a-1)=0π/201/sina>-1/cosasina>0,cosa<0所以sina<-cosasina+cosa<0√2sin(a+π/4)<0所以2a=11π/6舍去2a=7π/62a+π/3=3π/2所以sin(2a+π/3)=-1
为您推荐：
其他类似问题
扫描下载二维码1.sin10 ° sin30 ° sin50 ° sin70 ° 的值为?2.求证:tan(x+y)+tan(x-y)=(sin2x)/(cosx ×cosx-siny ×siny)3.已知函数f(x)=[1-√ (2) × sin(2x-π/4)]/cosx,若α为第四象限角,且tanα=-4/3,求f(α)的值.4.设函数f(x)=(sinwx+coswx)^2+2coswx*coswx(w>0)的最小正周期为2π/3.求w的值.若函数y=g(x)的图象是由y=f(x)的图象向右平移π/2个单位长度得到.求y=g(x)的单调增区间.请注明解体思路,计算过程和结果.
5题才给5分?楼主你也太抠了吧...（1)原式=sin10*sin30*cos(90-50)*cos(90-70)=sin10*1/2*cos20*cos40=1/2*sin10cos10cos20cos40/cos10=(1/2)*8sin10cos10cos20cos40/8cos10=(1/16)*4sin20cos20cos40/cos10=(1/16)*2sin40cos40/cos10=(1/16)*sin80/sin80=1/16（2）tan(x+y)+tan(x-y)=sin(x+y)/cos(x+y)+sin(x-y)/cos(x-y)=[sin(x+y)cos(x-y)+cos(x+y)sin(x-y)]/[cos(x+y)cos(x-y)]=sin2x/[(cosxcosy-sinxsiny)(cosxcosy+sinxsiny)]=sin2x/[(cosx)^2(cosy)^2-(sinx)^2(siny)^2]=sin2x/[(cosx)^2(cosy)^2-(1-(cosx)^2)(1-(cosy)^2)]=sin2x/[(cosx)^2+(cosy)^2-1]=sin2x/[(cosx)^2-(siny)^2]（3）题目没看懂?（4）1.f(x)=(sinwx+coswx)^2+2cos^2wx=1+sin2wx+1+cos2wx=2+根号2sin（2wx+π/4）T=2π/2w=2π/3,w=3/22.g（x）=2+根号2sin[3(x-π/2)+π/4]=2+根号2sin(3x-5π/4)令-π/2+2Kπ
为您推荐：
其他类似问题
扫描下载二维码