一道有难度的数学题目

sin(x+20)=cos(x-10)+cos(x+10)
sin[30-(10-x)]=cos(x-10)+cos(x+10)
cos(10-x)*sin30-cos30*sin(10-x)=cos(x-10)+cos(x+10)
cos(x-10)*sin30+sin(x-10)*cos30=cos(x-10)+cos(x+10)
sin(x-10)*cos30-cos(x-10)*sin30=cos(x+10)
sin(x-10)*sin60-cos(x-10)*cos60=cos(x+10)
-cos(x+50)=cos(x+10)
cos[(x+30)+20]+cos[(x+30)-20]=0
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2cos(x+30)*cos20=0
cos(x+30)=0
x=60+kπ k为整数
tanx=根号下3

sin(X+20) = sinXcos20 + cosXsin20
cos(X+10) = cosXcos10 - sinXsin10
cos(X-10) = cosXcos10 + sinXsin10
cos(X+10) + cos(X-10) = 2 cosXcos10
sinXcos20 + cosXsin20 = 2cosXcos10
两端同时除以cosX
tanX cos20 + sin20 = 2cos10
tanX
= (2cos10 - sin20)/cos20
= 2cos10(1-sin10)/cos20
= 1.732