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Question

The complete solution set of θ which satisfy the equation 2tanθcotθ=1 is
  1. {nππ4}{mπ+tan1(12)}; m,nZ
  2. {nπ+π4}{mπ±tan1(12)}; m,nZ 
  3. {mπ+tan1(12)},mZ
  4. {nππ4},nZ


Solution

The correct option is A {nππ4}{mπ+tan1(12)}; m,nZ
2tanθcotθ=1
For tanθ,cotθ to be defined, we get
θ(2n+1)π2,θnπ

Now, 
2tanθ1tanθ=12tan2θ+tanθ1=0(tanθ+1)(2tanθ1)=0tanθ=1,      tanθ=12θ=nππ4,      θ=mπ+tan112θ={nππ4}{mπ+tan1(12)}; m,nZ

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