Question 21 (A) - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Sept. 2, 2025 by Teachoo

This question is similar to Chapter 2 Class 12 Inverse Trigonometric Functions - Ex 2.1

Please check the question here

https://www.teachoo.com/3041/676/Ex-2.1--6---Find-principal-value-of-tan-1-(-1)---Chapter-2-Inverse/category/Ex-2.1/

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Transcript

Question 21 (A) Evaluate tan(tan^(−1) (−1)+𝜋/3)We have to find 𝐭𝐚𝐧(〖𝒕𝒂𝒏〗^(−𝟏) (−𝟏)+𝝅/𝟑) Let’s find tan^(−1) (−1) first 〖𝒕𝒂𝒏〗^(−𝟏) (−𝟏) Let y = tan−1 (−1) We know that tan−1 (−x) = − tan −1 x y = − tan−1 (1) y = − 𝝅/𝟒 Since Range of tan−1 is (−π/2,π/2) Hence, tan−1 (−1) = − 𝝅/𝟒 is correct Now, 𝒕𝒂𝒏(〖𝒕𝒂𝒏〗^(−𝟏) (−𝟏)+𝝅/𝟑) =𝑡𝑎𝑛((−𝜋)/4+𝜋/3) =𝒕𝒂𝒏(𝝅/𝟑−𝝅/𝟒) Using 𝑡𝑎𝑛(𝐴−𝐵)=(𝑡𝑎𝑛⁡𝐴 − 𝑡𝑎𝑛⁡𝐵)/(1 + 𝑡𝑎𝑛⁡𝐴 𝑡𝑎𝑛⁡𝐵 ) =(𝑡𝑎𝑛(𝜋/3) − tan⁡(𝜋/4))/(1 + 𝑡𝑎𝑛(𝜋/3) tan⁡(𝜋/4) ) =(√3 − 1)/(1 + √3 × 1) =(√3 − 1)/(1 + √3 ) =(√𝟑 − 𝟏)/(√𝟑 + 𝟏)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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