已知A B属于(3派/4 ,派), sin(A + B )= -3/5,sin(B-派/4)=12/13 ,则cos(A+ 派/4)=?
已知A B属于(3π/4 ,π), sin(A + B )= -3/5,sin(B-π/4)=12/13 ,则cos(A+ π/4)=?解:A B∈(3π/4 ,π), →(A + B )=∈(3π/2,2π)sin(A + B )= -3/5,→cos(A + B )= 4/5,B∈(3π/4 ,π), →(B-π/4)∈(π/2,3π/4)sin(B-π/4)=12/13 ,→cos(B-π/4)=-5/13 ,∴cos(A+ π/4)=cos[(A+B)-(B- π/4)]=cos(A+B)cos(B- π/4)+sin(A+B)sin(B- π/4)=(4/5)*((-5/13)+(-3/5)*(12/13)=-56/65
