Question

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}
]

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

Solution