If 3 tan-1 x + cot-1 x = π,

Question:

If 3 tan-1 x + cot-1 x = π, then x equals

(a) 0

(b) 1

(c) -1

(d) ½

Solution:

(b) 1

Given, 3 tan-1 x + cot-1 x = π

2 tan-1 x + tan-1 x + cot-1 x = π

2 tan-1 x + π/2 = π (As tan-1 + cot-1 = π/2)

2 tan-1 x = π/2

tan-1 x = π/4

x = 1

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