求值题.thanks.
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求值题.thanks.
14.求值:sin50°×〔1+(根号3)tan10°〕
14.求值:sin50°×〔1+(根号3)tan10°〕
![求值题.thanks.](/uploads/image/z/7190695-55-5.jpg?t=%E6%B1%82%E5%80%BC%E9%A2%98.thanks.)
sin50°[1+(√3)×tan10°]
=sin50×[(√3)sin10+cos10]/cos10
=(sin50/cos10)×2×(cos30sin10+cos10sin30)
=(sin50/cos10)×2×sin40
=2×sin50×cos50/cos10
=sin100/cos10
=cos10/cos10
=1
=sin50×[(√3)sin10+cos10]/cos10
=(sin50/cos10)×2×(cos30sin10+cos10sin30)
=(sin50/cos10)×2×sin40
=2×sin50×cos50/cos10
=sin100/cos10
=cos10/cos10
=1