2sin50 +sin10×(1+ √3tan10)

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2sin50+sin10×(1+√3tan10)2sin50+sin10×(1+√3tan10)2sin50+sin10×(1+√3tan10)2sin50°+sin10°×(1+√3tan10°)=

2sin50 +sin10×(1+ √3tan10)
2sin50 +sin10×(1+ √3tan10)

2sin50 +sin10×(1+ √3tan10)
2sin50° +sin10°×(1+ √3tan10°)
=2sin(60°-10°)+sin10°+√3tan10°sin10°
=2sin60°cos10°-2cos60°sin10°+sin10°+√3tan10°sin10°
=√3cos10°-sin10°+sin10°+√3tan10°sin10°
=√3cos10°+√3tan10°sin10°
=√3cos10°+√3(sin10°/cos10°)sin10°
=√3/cos10° (cos²10°+sin²10°)
=√3sec10°