Question

已知cosa=1/3,cos(a+b)=1 求证cos=(2a+b)=1/3

Answer 1

cos(2a+b)=cos[a+(a+b)]=cosacos(a+b)-sinasin(a+b)

由于cos(a+b)=1,所以sin(a+b)=0

将cosa=1/3,cos(a+b)=1,sin(a+b)=0代入cosacos(a+b)-sinasin(a+b)=(1/3)*1=1/3

故cos=(2a+b)=1/3