早教吧作业答案频道 -->数学-->
证明：sinA+1/(1+sina+cosa0=1/2tan(a/2)+1/2
题目详情
证明：sinA+1/(1+sina+cosa0=1/2tan(a/2)+1/2
▼优质解答
答案和解析
1+sina=sin²(a/2)+cos²(a/2)+2sin(a/2)*cos(a/2)=[sin(a/2)+cos(a/2)]²,
cosa=cos²(a/2)-sin²(a/2)=[cos(a/2)+sin(a/2)]*[cos(a/2)-sin(a/2)]
那么1+sina+cosa=[cos(a/2)+sin(a/2)]*[cos(a/2)-sin(a/2)+cos(a/2)+sin(a/2)]
=2cos(a/2)*[cos(a/2)+sin(a/2)]
所以(sina+1)/(1+sina+cosa)=[cos(a/2)+sin(a/2)]/2cos(a/2)
=[1+tan(a/2)]/2
=1/2*tan(a/2)+1/2
cosa=cos²(a/2)-sin²(a/2)=[cos(a/2)+sin(a/2)]*[cos(a/2)-sin(a/2)]
那么1+sina+cosa=[cos(a/2)+sin(a/2)]*[cos(a/2)-sin(a/2)+cos(a/2)+sin(a/2)]
=2cos(a/2)*[cos(a/2)+sin(a/2)]
所以(sina+1)/(1+sina+cosa)=[cos(a/2)+sin(a/2)]/2cos(a/2)
=[1+tan(a/2)]/2
=1/2*tan(a/2)+1/2
看了 证明：sinA+1/(1+s...的网友还看了以下：