Question

EXAMPLE 31 Prove that cot" (am ++ cot 1 (be + 1) + cot-* (2) = 0

11th - 12th Class

Maths

Solution

103

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SOLUTION We have [ begin{aligned} mathrm{LHS} &=tan ^{-1}left(frac{a-b}{1+a b}right)+tan ^{-1}left(frac{b-c}{1+b c}right)+tan ^{-1}left(frac{c-a}{1+c a}right) &=left(tan ^{-1} a-tan ^{-1} bright)+left(tan ^{-1} b-tan ^{-1} cright)+left(tan ^{-1} c-tan ^{-1} aright) &=0=R H S end{aligned} ]