分类：教育/科学-学习帮助
问题：已知0小于a小于派/2,派/2小于b小于派,且tana/2=1/? 
[1]ca和cosb的值;[2]tan[a-b]/2的值.
回答：tan a/2 = sin a/2  / c a/2  = 1/2 2 * sin  a/2  =  cos a/2,  2 sin a = cos^2 a/2 = (1+cos a)/24 sin a = 1 + cos a     ......  (1)       2tan(a/2)tan a＝——————= 4/3,        1－tan2(a/2)3 sin a = 4 cos a     .........(2)By (10 and (2) we have sin a = 4/13,   cos a = 3/13sin (a+b) = sin a  cos b  +  cos a sin b =  5 /134 cos b + 3 sin b =  5    ..... (3)cos b =  - \sqr( 1- sin^ 2 b )By (3) sin b = 3 / 5,  cos b =  - 4/5.tan b/2 =  (sin b ) / ( 1+ cos b ) = 3,tan ( a-b)/2 =   tan a/2 －tanb/2              ——————-----------             1＋tana/2 ·tanb/2 =( 1/2 - tan b/2) / ( 1+ 0.5 tan b/2)=-1