①已知Sina+COSa/Sina-COSa=3,求Sina,COSa的值;②已知π/2<b<a<3π/4,COS(a-b)=12/13②已知π/2小于b<a<3π/4,COS(a-b)=12/13,sin(a+b)=-3/5,求COS2b的值.
问题描述:
①已知Sina+COSa/Sina-COSa=3,求Sina,COSa的值;②已知π/2<b<a<3π/4,COS(a-b)=12/13
②已知π/2小于b<a<3π/4,COS(a-b)=12/13,sin(a+b)=-3/5,求COS2b的值.
答
(sina+cosa)/(sina-cosa)=3
sina+cosa=3sina-3cosa
sina=2cosa
(sina)^2+(cosa)^2=1
5(cosa)^2=1
cosa=(+/-)根号5/5
sina=(+/-)2根号5/5
∵π/2