Question

1.已知a,b都是锐角,cosa=1/7,cos(a+b)=-11/14,求cosb的值.(提示:b=(a+b)-a)

Answer 1

1、cosb=cos(a+b-a)=cos(a+b)cosa+sin(a+b)sina=-11/14*1/7+(5*根号3/14)*(4*根号3/7)=1/2

2、cosA=正负12/13 sinB=4/5

cosC=cos(PAI-(A+B))=-cos(A+B)=-(COSACOSB-SINASINB)=-16/65或者56/65

3、cos(a+b)=cosacosb-sinasinb=-根号5/3*(-3/4)-2/3*(-根号7/4)=(3根号5+2根号7)/12

sin(a-b)=sinacosb-cosasinb=2/3*(-3/4)-(-根号5/3)*(-根号7/4)=-(6+根号35)/12