α、β为锐角,2tanα+3sinβ =7,tanα-6sinβ=1,求sinα的值

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α、β为锐角,2tanα+3sinβ =7,tanα-6sinβ=1,求sinα的值
α、β为锐角,2tanα+3sinβ =7,tanα-6sinβ=1,求sinα的值

α、β为锐角,2tanα+3sinβ =7,tanα-6sinβ=1,求sinα的值
2tanα+3sinβ =7
tanα-6sinβ=1
4tanα+6sinβ =14
tanα-6sinβ=1
两式相加,消 sinβ
5tanα = 15
tanα = 3
两边平方
(tanα)^2 = 9
(sinα)^2 = 9 (cosα)^2
(sinα)^2 = 9 * [1 - (sinα)^2]
(sinα)^2 = 9/10
α 为锐角 ,所以
sinα = 3/√10