How to prove the following? $cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3$

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Answer 1 · 2017-03-01T15:11:39

$LHS=cot^-1 7+cot^-1 8+cot^-1 18$

$=cot^-1 ((7xx8-1)/(8+7))+cot^-1 18$

$=cot^-1 (55/15)+cot^-1 18$

$=cot^-1 (11/3)+cot^-1 18$

$=cot^-1 ((11/3xx18-1)/(11/3+18))$

$=cot^-1 ((66-1)/((11+18*3)/3))$

$=cot^-1 3=RHS$

How to prove the following? cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3