求值:(tan5-cos5/sin5)(cos20-1)/cos70
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2012-03-09 · 知道合伙人教育行家
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(tan5-cos5/sin5)(cos20-1) / cos70
= (sin5/cos5-cos5/sin5)[(1-2sin²10)-1] / cos(90-20)
= (sin²5-cos²5)/(cos5sin5) × 2sin²10 / sin20
= (-cos10)/(1/2 sin10) × 2sin²10 / (2sin10cos10)
= -1/2 cos10/sin10 × sin²10 / (sin10cos10)
= -1/2
= (sin5/cos5-cos5/sin5)[(1-2sin²10)-1] / cos(90-20)
= (sin²5-cos²5)/(cos5sin5) × 2sin²10 / sin20
= (-cos10)/(1/2 sin10) × 2sin²10 / (2sin10cos10)
= -1/2 cos10/sin10 × sin²10 / (sin10cos10)
= -1/2
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