M=sinα×tan（α/2）+cosα,N=tanπ/8(tanπ/8+2),

题目

M=sinα×tan（α/2）+cosα,N=tanπ/8(tanπ/8+2),
则M与N的大小关系是
A.M>N B.M=N C.M请写出详细过程

答案

M=sina X tan(a/2) +cosa
=2sin(a/2)cos(a/2)[sin(a/2)/cos(a/2)]+2cos(a/2)^2-1
=2sin(a/2)^2+2cos(a/2)^2-1
=2-1=1.
tan45=2tan22.5/(1-tan22.5^2)=1
解出tan22.5=根号2-1
带入N得N=2-1=1
M=N