Simplify  
cosθ
1 - tanθ
  +  
sinθ
1 - cotθ
 


Answer:

sinθ + cosθ

Step by Step Explanation:
  1. We have been asked to simplify the  
    cosθ
    1 - tanθ
      +  
    sinθ
    1 - cotθ
     .
  2. Now,  
    cosθ
    1 - tanθ
      +  
    sinθ
    1 - cotθ
     
    =  
    cosθ
    1 -  
    sinθ
    cosθ
     
      +  
    sinθ
    1 -  
    cosθ
    sinθ
     
     
    =  
    cos2θ
    cosθ - sinθ
      +  
    sin2θ
    sinθ - cosθ
     
    =  
    sin2θ
    sinθ - cosθ
      -  
    cos2θ
    sinθ - cosθ
     
    =  
    sin2θ - cos2θ
    sinθ - cosθ
     
    =  
    (sinθ - cosθ)(sinθ + cosθ)
    sinθ - cosθ
     
    = sinθ + cosθ
  3. Therefore,  
    cosθ
    1 - tanθ
      +  
    sinθ
    1 - cotθ
      is equal to the sinθ + cosθ.

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