MathematicsState whether the given statement is true or false. tanθ 1−tanθ − cotθ 1−cotθ = cosθ+sinθ cosθ−sinθ  

State whether the given statement is true or false.


tanθ 1tanθ cotθ 1cotθ = cosθ+sinθ cosθsinθ  


  1. A
    True
  2. B
    False 

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    Solution:

    Given the statement is tanθ 1tanθ cotθ 1cotθ = cosθ+sinθ cosθsinθ  .
    Considering,  tanθ 1tanθ + cotθ 1cotθ   , change tanθ= sinθ cosθ  and cotθ= cosθ sinθ .    tanθ 1tanθ cotθ 1cotθ = sinθ cosθ × cosθ cosθsinθ cosθ sinθ × sinθ sinθcosθ tanθ 1tanθ cotθ 1cotθ = sinθ cosθsinθ + cosθ cosθsinθ  
    Taking the LCM.  tanθ 1tanθ cotθ 1cotθ tanθ 1tanθ + cotθ 1cotθ = cosθ+sinθ cosθsinθ  
    Hence, tanθ 1tanθ + cotθ 1cotθ = cosθ+sinθ cosθsinθ  
    So the statement is true and the correct option is 1.
     
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