若 x∈[π/6,π/3]时,k+tan(2x-π/3)的值总不大于零,求实数k的取值范围.
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![若 x∈[π/6,π/3]时,k+tan(2x-π/3)的值总不大于零,求实数k的取值范围.](/uploads/image/z/1596283-43-3.jpg?t=%E8%8B%A5+x%E2%88%88%5B%CF%80%2F6%2C%CF%80%2F3%5D%E6%97%B6%2Ck%2Btan%282x-%CF%80%2F3%29%E7%9A%84%E5%80%BC%E6%80%BB%E4%B8%8D%E5%A4%A7%E4%BA%8E%E9%9B%B6%2C%E6%B1%82%E5%AE%9E%E6%95%B0k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
若 x∈[π/6,π/3]时,k+tan(2x-π/3)的值总不大于零,求实数k的取值范围.
若 x∈[π/6,π/3]时,k+tan(2x-π/3)的值总不大于零,求实数k的取值范围.
若 x∈[π/6,π/3]时,k+tan(2x-π/3)的值总不大于零,求实数k的取值范围.
当x∈[π/6,π/3]时,2x-π/3∈[0,π/3]
所以tan(2x-π/3)∈[0,√3〕
因为k+tan(2x-π/3)≤0
所以k+√3≤0
所以k≤-√3