三角恒等变换题。谢谢!
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4sin²55°+cos10°-tan160°·sin170°
=4sin²55°-2+2+cos10°+tan20°sin10°
=-2cos110°+2+cos10°+tan20°sin10°
=2sin20°+2+cos10°+sin20°sin10°/cos20°
=2sin20°+2+cos10°(1+2sin²10°/cos20°)
=2sin20°+2+cos10°(cos20°+2sin²10°)/cos20°
=2sin20°+2+cos10°/cos20°
=(sin40°+cos10°)/cos20°+2
=[sin(30°+10°)+cos10°]/cos20°+2
=[3cos10°+√3sin10°]/2cos20°+2
=2√3sin(60°+10°)/2cos20°+2
=√3cos20°/cos20°+2
=2+√3
=4sin²55°-2+2+cos10°+tan20°sin10°
=-2cos110°+2+cos10°+tan20°sin10°
=2sin20°+2+cos10°+sin20°sin10°/cos20°
=2sin20°+2+cos10°(1+2sin²10°/cos20°)
=2sin20°+2+cos10°(cos20°+2sin²10°)/cos20°
=2sin20°+2+cos10°/cos20°
=(sin40°+cos10°)/cos20°+2
=[sin(30°+10°)+cos10°]/cos20°+2
=[3cos10°+√3sin10°]/2cos20°+2
=2√3sin(60°+10°)/2cos20°+2
=√3cos20°/cos20°+2
=2+√3
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