已知向量a=(cosα,1+sinα),b=(1+cosα,sinα),若绝对值a+b=根号3,求sinαcosα的值
题目
已知向量a=(cosα,1+sinα),b=(1+cosα,sinα),若绝对值a+b=根号3,求sinαcosα的值
已知向量a=(cosα,1+sinα),b=(1+cosα,sinα),
若绝对值a+b=根号3,求sinαcosα的值
答案
等式两边同时平方可得:
(1+2cosα)^2+(1+2sinα)^2=3
1+4cosα+4(cosα)^2+1+4sinα+4(sinα)^2=3
cosα+sinα=-3/4,再平方得:
1+2sinαcosα=9/16
sinαcosα=-7/32
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