Question

已知a为锐角,cosa=3/5,tan(a-b)=1/3,求tana,tanb

Answer 1

a为锐角,cosa=3/5,
则sina=4/5,tana=4/3.
tanb=tan[a-(a-b)]=[ tan a- tan(a-b)]/[1+ tan atan(a-b)]
=9/13.

Answer 2

a为锐角，cos a=3/5,所以sin a=4/5
tan a=4/3
tan a=tan (a-b+b)=(tan(a-b)+tan b)/(1-tan(a-b)tan b)
带入，tan b=9/13