cot(π/4+a/2)+tana=?A.secaB.cscaC.cosaD.sina）

Question

cot(π/4+a/2)+tana=?A.seca B.csca C.cosa D.sina ）

Answer 1

选A
COS(π/4+a/2)
------------- + sina/cosa
sin(π/4+a/2)
=cos(π/4)cos(a/2)-sin(π/4)sin(a/2)
___________________________________ +sina/cosa
sin(π/4)cosa/2+cosπ/4sina/2
=cos(a/2)-sin(a/2)
-------------------+sina/cosa
cos(a/2)+sin(a/2)
然后把sina/cosa前面这片复杂的分式分子分母同时乘cos(a/2)+sin(a/2)
=cos^(a/2)-sin^(a/2)
------------------------------------
cos^(a/2)+sin^(a/2)+2sin(a/2)cos(a/2) +sina/cosa
=cosa
------+sina/cosa
1+sina
=cos^a+sin^a+sina
-------------------
cosa(sina+1)
=1+sina
--------
cosa(sina+1)
1
=--------=seca
cosa