If cot α = √2 + 1, then the value of tan α - cot α = ?

Question

Question

This question was previously asked in

RRB ALP CBT I 30 Aug 2018 Shift 3 Official Paper

Answer 1

Given:

\(cot \alpha = {\sqrt2 + 1}\)

Concept used:

1. tan θ = 1/cot θ

2. a² - b² = (a + b)(a - b)

Calculation:

\(cot \alpha = {\sqrt2 + 1}\) ....(1)

⇒ \(tan \alpha = \frac {1}{\sqrt2 + 1}\)

⇒ \(tan \alpha = \frac {(\sqrt2 - 1)}{(\sqrt2 + 1)(\sqrt2 - 1)}\)

⇒ \(tan \alpha = \frac {(\sqrt2 - 1)}{2 - 1}\)

⇒ \(tan \alpha = {(\sqrt2 - 1)}\) ....(2)

Now, (2) - (1),

tan α - cot α = \({(\sqrt2 - 1)} - {(\sqrt2 + 1)}\)

⇒ tan α - cot α = -2

∴ The required value is -2.