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sin40(tan10-3^1/2)=sin40(tan10-tan60)=-sin40{tan(60-10)*(1+tan60*tan10)=-sin50*(1+3^1*sin10/cos10)=-(sin50/cos10)*2*(1/2*cos10+3^1/2*sin10)=-(sin50/cos10)*2*(sin30*cos10+cos30*sin10)==-(sin50/cos10)*2...
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