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
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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

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