Simplify  
cosθ - 2 cos3θ
2 sin3θ - sinθ
 


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Answer:

cot θ

Step by Step Explanation:
  1. Let,
    S =  
    cosθ - 2 cos3θ
    2 sin3θ - sinθ
     
  2. On taking sinθ and cosθ common,
    ⇒ S =  
    cosθ (1 - 2 cos2θ)
    sinθ (2 sin2θ - 1)
     
    ⇒ S =  
    cosθ [(1 - cos2θ) - cos2θ]
    sinθ [sin2θ + (sin2θ - 1)]
     
  3. Using identity: sin2θ + cos2θ = 1
    ⇒ S =  
    cosθ [sin2θ - cos2θ]
    sinθ [sin2θ - cos2θ]
     
    ⇒ S = cot θ

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