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Question : 24 of 160
Marks:
+1,
-0
Solution:
Consider the expression,
2k=n(n+1) Then
cot(Cot−1(1+n(n+1)))=Tan−1(‌‌) This implies
tan−1(‌‌)=tan−1(n+1)−tan−1n =(tan−14−tan−13+(tan−15−tan−14))+... &+(tan−133−tan−232) =tan−133−tan−13 =tan−1[‌‌] Further simplify the above
tan−1(‌‌)=tan−1(‌‌) cot(tan−1(‌‌))=cot(tan−1(‌‌)) cot[cot−1(‌‌)]=‌‌
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