关于三角恒等式

cos(a-b)=cosacosb+sinasinb=1/4
cos(a+b)=cosacosb-sinasinb=2/3
所以sinasinb=-5/24 cosacosb=11/24
tanatanb=sinasinb/cosacosb=-5/24/(11/24)=-5/11
-π/4＜a-b＜0π＜a+b＜3π/2
所以sin(a-b)=-√(1-cos^2(a-b)=-5/13
cos(a+b)=-√(1-sin^2(a+b)=-4/5
cos2a=cos[(a-b)+(a+b)]=cos(a-b)cos(a+b)-sin(a-b)sin(a+b)
=12/13*(-4/5)+5/13*(-3/5)=-63/65
sin2b=sin[(a+b)-(a-b)]=sin(a+b)cos(a-b)-cos(a+b)sin(a-b)
=-3/5*12/13-4/5*5/13=-56/65