Question
Question: If 1\< x \<\(\sqrt{2}\), then number of solutions of the equation tan<sup>–1</sup>(x – 1) + tan<sup...
If 1< x <2, then number of solutions of the equation
tan–1(x – 1) + tan–1 x + tan–1(x + 1) = tan–1 3x, is/are
A
0
B
1
C
2
D
3
Answer
0
Explanation
Solution
Given equation can be written as
tan–1 (x – 1) + tan–1 (x + 1) = tan–1 3x – tan–1 x
̃ tan–1 1−(x−1)(x+1)x−1+x+1 = tan–1 1+3x23x−x
̃ 2−x22x=1+3x22x
̃ x + 3x3 = 2x – x3
̃ 4x3 – x = 0
̃ x(4x2 – 1) = 0
̃ x = 0, x = ± ½
none of which satisfies 1 < x < 2