作业帮求cos15°-tan15°/cos15°+sin15°
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/14 23:58:02
求cos15°-tan15°/cos15°+sin15°
求cos15°-tan15°/cos15°+sin15°
求cos15°-tan15°/cos15°+sin15°
是 (cos 15°-tan 15°) / (cos 15°+sin 15°) 吗?
= = = = = = = = =
因为 sin 15°=sin (45°-30°)
=sin 45°cos 30°-cos 45°sin 30°
=(根号2) /2 *(根号3) /2 -(根号2) /2 *(1/2)
=(根号6 -根号2) /4,
cos 15°=cos (45°-30°)
=cos 45°cos 30°+sin 45°sin 30°
=(根号2) /2 *(根号3) /2 +(根号2) /2 *(1/2)
=(根号6 +根号2) /4,
tan 15°=sin 15°/cos 15°
=(根号6 -根号2) /(根号6 +根号2)
=2 -根号3,
所以 cos 15°-tan 15°=(根号6 +根号2 +4根号3 -8) /4,
cos 15°+sin 15°=(根号6) /2.
所以 原式=(根号6 +根号2 +4根号3 -8) / [2 (根号6)]
=(6 +2根号3 +12根号2 -8根号6) /12
=根号2 +(根号3) /6 -(2/3)(根号6) +1/2.
= = = = = = = = = =
以上计算可能有误,你最好检查一下.
15°和75°也是特殊角.
注意：
tan 15°=2 -根号3,
tan 75°=2 +根号3.
以后学 直线的斜率 时会用到.
sin30°=sin2*15 ° =2sin15° cos15° =1/2 sin15° cos15° =1/4
cos30°=cos2*15°=2(cos15°)^2-1=√3/2 (cos15°)^2=√3/4+1/2
tan15° =sin15° cos15° /cos15° cos15° =1/(√3+2)=2-√3
c...
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sin30°=sin2*15 ° =2sin15° cos15° =1/2 sin15° cos15° =1/4
cos30°=cos2*15°=2(cos15°)^2-1=√3/2 (cos15°)^2=√3/4+1/2
tan15° =sin15° cos15° /cos15° cos15° =1/(√3+2)=2-√3
cos15°-tan15°/cos15°+sin15°
=(cos15° cos15°-tan15 ° +sin15° cos15°)/cos15 °
=5(3√3-5)/2
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