mshd.net
当前位置:首页 >> (sin75+Cos75)/(Cos15%sin15)=? >>

(sin75+Cos75)/(Cos15%sin15)=?

见图

sin75+cos75 =sin75+sin15 =2sin(75+15)/2cos(75-15)/2 =2sin45cos30 =√6/2 sin75-cos75 =sin75-sin15 =2cos(75+15)/2sin(75-15)/2 =2cos45sin30 =√2/2 (sin75度+cos75度)/(sin75度-cos75度) =√6/2 / √2/2 =√3

0.5

sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30°=(√6+√2)/4 cos75=cos(30+45)=cos30cos45-sin30sin45=√6/4-√2/4=(√6-√2)/4

套公式cos(A-B)=cosA*cosB+sinA*sinB 上题等于cos60=0.5

显然sin105°=sin(180°-105°)=sin75° 而cos105°= -cos(180°-105°)= -cos75° 所以 sin105°cos105°+cos75°sin75° = -sin75°cos75°+cos75°sin75° =0

原式=【sin(75°+10°)-cos75°sin10°】/【cos(75°-10°)-sin75°sin10°】 =(sin75°cos10°+cos75°sin10°-cos75°sin10°)/(cos75°cos10°+sin75°sin10°-sin75°sin10°) =(sin75°cos10°)/(cos75°cos10°) =tan75° =tan(45°+30°) =(tan45°+tan30°)/(1-tan45°...

和差化积公式: sin15°+sin75° =2sin[(15°+75°)/2]cos[(15°-75°)/2] =2sin45°cos(-30°) =2sin45°cos30° =2×(√2/2)×(√3/2) =√6/2 或者sin15°+sin75° =sin(45°-30°)+sin(45°+30°) =(sin45°cos30°-sin30°cos45°)+(sin45°cos30°+sin30°cos45°...

sin15°cos75° =(根号6-根号2)/4X(根号6+根号2)/4 =[(根号6-根号2)X(根号6+根号2)]/16 =(6-2)/16 =1/4

COS75度等于COS15度,分母分子同时除以COS15度后得Tan15度+1,Tan15度等于Tan(45-30),所以最后答案等于3-根号3

网站首页 | 网站地图
All rights reserved Powered by www.mshd.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com