1.{cos40°+sin50°*（1+根号3*tan10°）}\{sin70°*根号（1+cos40°）}
={cos40+sin50*[(tan60-tan10)/tan(60-10)]}/{sin70*√[1+2cos^2(20)-1]
=[cos40+cos50*sin50/(cos60*cos10)]/[sin70cos20*√2]
=[cos40+sin100/(2*1/2*sin80)]/[sin70cos20*√2]
=[cos40+1]/(sin70cos20*√2)
=[2cos^2(20)-1+1]/[cos^2(20)*√2]
=√2.
2)：{2*sin50°+sin10°*（1+根号3*tan10°）}*根号（2*（sin80°）^2)
={2sin50+sin10*[(tan60-tan10)/tan(60-10)]}*√[2sin^2(80)]
={2sin50+sin10*cos50/(cos60*cos10)}*sin80*√2
={2sin50*sin80+2cos50*sin10}*√2
=2(sin50*cos10+cos50*sin10)*√2
=2*sin60*√2
=√6.
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