求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
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求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
求(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)的值
sin8°+sin7°cos15°
=sin(15°-7°) +sin7°cos15°
=sin15°cos7°-sin7°cos15°+sin7°cos15°
=sin15°cos7°
cos8°-sin7°sin15°
=cos(15°-7°) -sin7°sin15°
=cos15°cos7°+sin7°sin15°-sin7°sin15°
=cos15°cos7°
故
(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)
=sin15°cos7°/cos15°cos7°
=tan15°
(sin8°+sin7°cos15°)/(cos8°-sin7°sin15°)
=(sin(15-7)+sin7cos15)/(cos(15-7)-sin7sin15)
=(sin15cos7-cos15sin7+sin7cos15)/(cos15cos7+sin15sin7-sin15sin7)
=(sin15cos7)/(cos15cos7)
=tan15
tan30=2tan15/(1-(tan15)^2)=根号3/3,由此算出tan15