求【2sin50度+sin10度(1+根号3tan10度)】sin80度的值

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求【2sin50度+sin10度(1+根号3tan10度)】sin80度的值
求【2sin50度+sin10度(1+根号3tan10度)】sin80度的值

求【2sin50度+sin10度(1+根号3tan10度)】sin80度的值
【2sin50°+sin10°(1+根号3tan10°)】sin80°
=【2sin50°+sin10°(1+tan60°tan10°)】sin80°
=【2sin50°+sin10°(1+sin60°sin10°/cos60°cos10°)】sin80°
=【2sin50°+sin10°((cos60°cos10°+sin60°sin10°)/cos60°cos10°)】sin80°
=【2sin50°+sin10°((cos50°)/cos60°cos10°)】sin80°
=【2sin50°+2sin10°cos50°/cos10°】sin80°
=【(2sin50°cos10°+2sin10°cos50°)/cos10°】sin80°
=[2sin60°/cos10°]sin80°
=√3sin80°/cos10°
=√3sin80°/sin80°
=√3