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

Question

Nandana · Answer

hi here, ∫cosx/tanx dx = ∫ cos 2 x/ sinx dx =∫1-sin 2 x /sinx dx =∫1/sinx dx – ∫ sinx dx = ∫ cscx dx + cosx ∫ cscx dx = ∫ (csc 2 x +cotx cscx)/ (cscx+cotx)dx u =cscx+cotx du = -(cotxcscx+csc 2 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 · Answer

∫cosx/tanx dx = ∫ cos 2 x/ sinx dx =∫1-sin 2 x /sinx dx =∫1/sinx dx – ∫ sinx dx = ∫ cscx dx + cosx ∫ cscx dx = ∫ (csc 2 x +cotx cscx)/ (cscx+cotx)dx u =cscx+cotx du = -(cotxcscx+csc 2 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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Integrate the following question and kindly simplify the answer Integrate cosx/tanx

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

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