已知sina-sinb=-1/3,cosa-cosb=1/2,求cos(a-b)的值
假如还要求sin(a-b)的话,是一解还是两解?
人气:437 ℃ 时间:2019-12-09 01:18:58
解答
sina-sinb=-1/3 两边都平方,得(sina)^2+(sinb)^2-2sinasinb=1/9(1)
同理,得,(cosa)^2+(cosb)^2-2cosacosb=1/4(2)
(sina)^2+(cosa)^2=1,(sinb)^2+(cosb)^2=1(公式)
(1)+(2),整理得,sinasinb+cosacosb=59/72
cos(a-b)
=sinasinb+cosacosb
=59/72
有两解
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