3tan-1 x + cot-1 x = π then x equal to1. 1/22. -13. 14. 0

1.	3tan-1 x + cot-1 x = π then x equal to1. 1/22. -13. 14. 0
Answer» Correct Answer - Option 3 : 1 Concept: cos-1 x = \(π\over2\) - sin-1 x cot-1 x = \(π\over2\) - tan-1 x sec^-1 x = \(π\over2\) - cosec^-1 x Calculation: Given 3tan-1 x + cot-1 x = π ∵ cot-1 x = \(π\over2\) - tan-1 x 3tan-1 x + (\(π\over2\) - tan-1 x) = π 2tan^-1 x + \(π\over2\) = π 2tan^-1 x = \(\pi\over2\) tan^-1 x = \(\pi\over4\) x = tan \(\pi\over4\) = 1

Answer» Correct Answer - Option 3 : 1

Concept:

cos-1 x = \(π\over2\) - sin-1 x

cot-1 x = \(π\over2\) - tan-1 x

sec^-1 x = \(π\over2\) - cosec^-1 x

Calculation:

Given 3tan-1 x + cot-1 x = π

∵ cot-1 x = \(π\over2\) - tan-1 x

3tan-1 x + (\(π\over2\) - tan-1 x) = π

2tan^-1 x + \(π\over2\) = π

2tan^-1 x = \(\pi\over2\)

tan^-1 x = \(\pi\over4\)

x = tan \(\pi\over4\) = 1

Discussion