题目

已知α为锐角,且点（cosα,sinα）在曲线6x^2+y^2=5上,（1）求cos2α（2）求tan(2α-π/4）的值

提问时间：2020-10-10

答案

你好!
由题意
6cos²α + sin²α = 5
又 cos²α+sin²α =1
解得 cos²α = 4/5 sin²α = 1/5
cos(2α) = cos²α - sin²α = 3/5
(2)∵α是锐角
∴π/2 < 2α < π
sin(2α) >0
tan(2α) = sin(2α) / cos(2α)
= √(1 - cos²2α) / cos(2α)
= 4/3
tan(2α - π/4)
= [ tan(2α) - tan(π/4) ] / [ 1+ tan(2α) tan(π/4) ]
= (4/3 - 1) / (1 + 4/3 *1)
= 1/7