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Integrate the following question and kindly simplify the answer Integrate cosx/tanx

Integrate the following question and kindly simplify the answer Integrate cosx/tanx

Grade:12

2 Answers

Nandana
110 Points
3 years ago
hi
  here,
   ∫cosx/tanx dx = ∫ cos2 x/ sinx dx
                           =∫1-sin2 x /sinx dx
                           =∫1/sinx dx – ∫ sinx dx
                           = ∫ cscx dx + cosx
                  
                ∫ cscx dx = ∫ (csc2x +cotx cscx)/ (cscx+cotx)dx
                               
                                     u =cscx+cotx
                                    du = -(cotxcscx+csc2 x) dx
                               = -∫1/u du
                               = -lnu = ln(1/u) = ln(1/(cscx+cotx))
           
       ∫cosx/tanx dx = ln(1/(cscx+cotx)) +cosx +C is the answer !
amj
41 Points
3 years ago
 
 ∫cosx/tanx dx = ∫ cos2 x/ sinx dx
                           =∫1-sin2 x /sinx dx
                           =∫1/sinx dx – ∫ sinx dx
                           = ∫ cscx dx + cosx
                  
                ∫ cscx dx = ∫ (csc2x +cotx cscx)/ (cscx+cotx)dx
                               
                                     u =cscx+cotx
                                    du = -(cotxcscx+csc2 x) dx
                               = -∫1/u du
                               = -lnu = ln(1/u) = ln(1/(cscx+cotx))
           
       ∫cosx/tanx dx = ln(1/(cscx+cotx)) +cosx +C is the answer !

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