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 August 14, 2026 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/

[SQP 2026] Evaluate tan(tan^(−1) (−1)+𝜋/3) - Sample Paper Class 12 - CBSE Class 12 Sample Paper for 2026 Boards

part 2 - Question 21 (A) - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 21 (A) - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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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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