Question

sin(a-b)sin(b-y)-cos(a-b)cos(y-b)为什么等于-cos(a-y)

sin(a-b)sin(b-y)-cos(a-b)cos(y-b)为什么等于-cos(a-y)

Answer 1

cos(a+b)=cosacosb-sinasinb
所以原式=-[cos(a-b)cos(b-y)-sin(a-b)sin(b-y)]
=-cos[(a-b)+(b-y)]
=-cos(a-y)

Answer 2

设为x/a+y/b=1
a>0,b>0
则2/a+1/b=1
ab=ab(2/a+1/b)
=2b+a≥2√(ab)
当2b=a时取等号
则1/b+1/b=1
b=2,a=4
所以直线是x+2y-4=0