己知sina+cosa=2/3,求sin2a值?己知sina *cosa=60/169,且丌/4<a<丌/2,求sina,cosa的值?

问题描述:

己知sina+cosa=2/3,求sin2a值?己知sina *cosa=60/169,且丌/4<a<丌/2,求sina,cosa的值?

(1) sina+cosa=2/3,所以(sina+cosa)^2=4/9,即1+2sina *cosa=4/9,
所以sin2a=2sina *cosa=-5/9.
(2) 丌/4<a<丌/2,则丌/2<2a<丌,sina>0,cosa>0,cos2asin2a=2sina *cosa=2*60/169=120/169,cos2a=-119/169
cos2a=1-(2sina)^2=-119/169,sina=12/13;
所以cos=5/13