化简sin100°(1+√3tan10°)/√(2cos^2 50°)..

sin100°(1+√3tan10°)/√(2cos²50°)
=sin(90°+10°)(1+√3tan10°)/[√2 * cos(60°-10°)]
=cos10°(1+√3tan10°)/[√2 * (cos10°/2 + √3sin10°/2)]
=√2(cos10°+√3sin10°)/(cos10°+√3sin10°)
=√2

1+√3tan10°=(cos10++√3sin10)/cos10
=2(sin30cos10+cos30sin10)/cos10
=2sin40/cos10
sin100°(1+√3tan10°)/√(2cos^2 50°)
=sin100°(1+√3tan10°)/(√2)cos 50°)

=√2sin100sin40/[coc10cos50]

=√2coc10cos50/[(coc10cos50]

=√2