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Question
If x, y, z are positive, then prove that
`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`
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Solution
LHS = `tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx"))`
`= tan^-1 "x" - tan^-1"y" + tan^-1"y" - tan^-1"z" + tan^-1"z" - tan^-1"x"` .......[∵ x > 0, y > 0, z > 0]
= 0
= RHS
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