化简sin50°(1+根号下3×tan10°) 急！要过程！谢谢！
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sin50°(1+根号3×tan10°)
=sin50°(1+tan60°×tan10°)
=sin50°(tan60°-tan10°)/tan(60°-10°)
=sin50°(tan60°-tan10°)/tan(50°)
=(tan60°-tan10°)cos50°
=(sin60°/cos60° - sin10°/cos10°)cos50°
=[(sin60°cos10°-sin10°cos60°)/cos60°cos10°]cos50°
=[sin50°/cos60°cos10°]cos50°
=sin50°cos50°/cos60°cos10°
=sin100°/2cos60°cos10°
=sin100°/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1
=sin50°(1+tan60°×tan10°)
=sin50°(tan60°-tan10°)/tan(60°-10°)
=sin50°(tan60°-tan10°)/tan(50°)
=(tan60°-tan10°)cos50°
=(sin60°/cos60° - sin10°/cos10°)cos50°
=[(sin60°cos10°-sin10°cos60°)/cos60°cos10°]cos50°
=[sin50°/cos60°cos10°]cos50°
=sin50°cos50°/cos60°cos10°
=sin100°/2cos60°cos10°
=sin100°/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1
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