This question was previously asked in

UP TGT Mathematics 2021 Official Paper

Option 2 : \(\dfrac{\pi}{3}\)

CT 1: हिन्दी (आदिकाल)

6220

10 Questions
40 Marks
10 Mins

__Formula used:__

\(If\ A>B,\ then \ tan(\frac{A-B}{2})=\frac{a-b}{a+b}cos \frac{C}{2}\)

**Calculations:**

Given, In ΔABC, a = 2b and \(|A-B|=\dfrac{\pi}{3}\)

Here A > B,

\(tan(30^0)=\frac{2b-b}{2b+b} \ cot \frac{C}{2}\)

⇒ \(\frac{1}{\sqrt{3}}=\frac{1}{3}cot \frac{C}{2}\)

⇒ \(\frac{3}{\sqrt{3}}=cot \frac{C}{2}\)

⇒ \({\sqrt{3}}=cot \frac{C}{2}\)

⇒ \( \frac{C}{2}=cot^{-1}({\sqrt{3}})\)

⇒ \( \frac{C}{2}=\frac{\pi}{6}\)

⇒ \({C}=\frac{\pi}{3}\)

**Hence**, the correct answer is option **2)**.