cosα+2sinα=-√5
(cosα+2sinα)²=5
cos²α+4cosαsinα+4sin²α=5
(cos²α+4cosαsinα+4sin²α)/(cos²α+sin²α)=5
等式左边分子分母同时除以cos²α整理可得
(4tan²α+4tanα+1)/(tan²α+1)=5
4tan²α+4tanα+1=5(tan²α+1)
(tanα-2)²=0
tanα=2

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