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Complete solution set of [cot^(-1)x]+2[t...

Complete solution set of `[cot^(-1)x]+2[tan^(-1)x]=0,` where `[]` denotes the greatest integer function, is equal to (a)`(0,cot1)` (b) `(0,tan1)` `(tan1,oo)` (d) `(cot1,tan1)`

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To solve the equation \([cot^{-1}x] + 2[tan^{-1}x] = 0\), where \([]\) denotes the greatest integer function, we will break down the problem step by step. ### Step 1: Understanding the Equation We need to analyze the equation \([cot^{-1}x] + 2[tan^{-1}x] = 0\). This means that the sum of the greatest integer values of \(cot^{-1}x\) and twice the greatest integer value of \(tan^{-1}x\) must equal zero. ### Step 2: Setting Up Cases Since the greatest integer function can take integer values, we can set up cases based on possible values of \([cot^{-1}x]\) and \([tan^{-1}x]\). ...
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