早教吧作业答案频道 -->数学-->
求值:sin50(1+根号3tan10)-cos20/cos80根号(1-cos20)
题目详情
求值:【sin50(1+根号3tan10)-cos20】/cos80根号(1-cos20)
▼优质解答
答案和解析
(sin50°(1+√3*tan10°)-cos20°)/(cos80°*√(1-cos20°))
=(sin50°(1+√3*sin10°/cos10°)-cos20°)/(cos80°*√(1-cos20°))
=(sin50°((cos10°+√3*sin10°)/cos10°)-cos20°)/(cos80°*√(2(sin10°)^2))
=(sin50°((1/2)cos10°+(√3/2)*sin10°)/((1/2)*cos10°)-cos20°)/(cos80°*√(2(sin10°)^2))
=(sin50°(sin30°*cos10°+cos30°*sin10°)/(1/2)*cos10°-cos20°)/((√2)cos80°*sin10°)
=(sin50°*sin40°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=(sin50°*cos50°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)sin100°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)sin80°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)cos10/(1/2)*cos10°-cos20°)/((√2)sin10°sin10°)
=(1-cos20°)/((√2)sin10°sin10°)
=2(sin20°)^2/(√2)(sin20°)^2
=2/√2
=√2
=(sin50°(1+√3*sin10°/cos10°)-cos20°)/(cos80°*√(1-cos20°))
=(sin50°((cos10°+√3*sin10°)/cos10°)-cos20°)/(cos80°*√(2(sin10°)^2))
=(sin50°((1/2)cos10°+(√3/2)*sin10°)/((1/2)*cos10°)-cos20°)/(cos80°*√(2(sin10°)^2))
=(sin50°(sin30°*cos10°+cos30°*sin10°)/(1/2)*cos10°-cos20°)/((√2)cos80°*sin10°)
=(sin50°*sin40°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=(sin50°*cos50°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)sin100°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)sin80°/(1/2)*cos10°-cos20°)/((√2)sin10°*sin10°)
=((1/2)cos10/(1/2)*cos10°-cos20°)/((√2)sin10°sin10°)
=(1-cos20°)/((√2)sin10°sin10°)
=2(sin20°)^2/(√2)(sin20°)^2
=2/√2
=√2
看了 求值:sin50(1+根号3...的网友还看了以下:
直线AB过点A(m,0)、B(0,n)(m>0,n>0),反比例函数y=m/x的图像与AB交于C、 2020-04-08 …
证明C(0,n)^2+C(1,n)^2+……+C(n,n)^2=C(n,2n) 2020-04-26 …
二次函数y=ax²+bx+c的图像如图所示,若M=4a+2b+c,N=a-b+c,P=4a+2b, 2020-05-16 …
排列组合公式A与C的换算技巧问题?A(m,n)一个是上标一个是下标,呵呵~C(0,n)=1A(0, 2020-06-09 …
直线L经过三点A(m,0),B(0,n),C(1,3),且m,n是正整数,求直线L的方向式方程 2020-06-12 …
已知数列{an}的通项公式为an=2^(n-1)+1则a1Cn^0+a2Cn^1+a3Cn^2+. 2020-07-09 …
∑[k=0,∞]C(k,N)C(n-k,M-N)=C(n,M)∑[k=0,n](1-p)^k=1/ 2020-07-16 …
已知点A(0,1/n),B(0,-1/n),C(4+1/n,0),其中n为正整数,设Sn表示△AB 2020-07-18 …
1.在△ABC中,tanA·(sinB)^2=tanB·(sinA)^2,那么三角形ABC一定是答 2020-08-02 …
孩子不懂,只好求助朋友们啦,先谢谢^O^二次函数y=ax²+bx+c的图象如图一所示,若M=4a+2 2021-01-22 …