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If cot​X +cotY=a tanX +tanY=b X+Y=Z then prove that , (a-b)tanZ=ab

If   cot​X +cotY=a
     tanX +tanY=b
         X+Y=Z
then prove that  ,
     (a-b)tanZ=ab

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
5 years ago
tanZ=tanx+tany/1-tanxtany=b/1-tanxtany
cotx+coty=tanx+tany/tanxtany=a
or tanxtany=b/a
so, tanZ=b/1-b/a=ab/a-b
so that   (a-b)tanZ=ab
hence proved
 

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