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Question Number 105414 by qwertyu last updated on 28/Jul/20

Commented by qwertyu last updated on 28/Jul/20

$$\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}$$

Commented by PRITHWISH SEN 2 last updated on 28/Jul/20

$$\frac{1}{1+\cot 1}+\frac{1}{1+\cot 89}+\frac{1}{1+\cot 5}+\frac{1}{1+\cot 85}+....$$$$...+\frac{1}{1+\cot 41}+\frac{1}{1+\cot 49}+\frac{1}{1+\cot 45}$$$$=\frac{1}{1+\cot 1}+\frac{1}{1+\tan 1}+\frac{1}{1+\cot 5}+\frac{1}{1+\tan 5}+....$$$$..+\frac{1}{1+\cot 41}+\frac{1}{1+\tan 41}+\frac{1}{1+1}$$$$=(\frac{1}{1+\cot 1}+\frac{\cot 1}{1+\cot 1})+(\frac{1}{1+\cot 5}+\frac{\cot 5}{1+\cot 5})+....$$$$..+(\frac{1}{1+\cot 41}+\frac{\cot 41}{1+\cot 41})+\frac{1}{2}$$$$=11+\frac{1}{2}=11\frac{1}{2}$$

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