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Question 21 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

Express sin -1 ⁡((sin⁡x  + cos⁡x)/√2); where (-π)/4 < 𝑥 < π/4 , in the simplest form.

Transcript

Question 21 (OR 1st Question) Express sin^(−1)⁡((sin⁡𝑥 + cos⁡𝑥)/√2); where (−𝜋)/4 < 𝑥 < 𝜋/4 , in the simplest form. sin^(−1)⁡((sin⁡𝑥 + cos⁡𝑥)/√2) = sin^(−1)⁡(sin⁡𝑥/√2+cos⁡𝑥/√2) = sin^(−1)⁡(sin⁡𝑥×1/√2+cos⁡𝑥×1/√2) = sin^(−1)⁡(sin⁡𝑥×cos⁡〖𝜋/4〗+cos⁡𝑥×s𝑖𝑛⁡〖𝜋/4〗 ) We know that sin (A + B) = sin A cos B + cos A sin B = sin^(−1)⁡(sin⁡(𝑥+𝜋/4) ) = sin^(−1)⁡(sin⁡(𝑥+𝜋/4) ) Now, checking if angle is in principal value i.e. 0<𝑥+𝜋/4<𝜋/2 i.e. (−𝜋)/4 < 𝑥 < 𝜋/4 which is true So, we can write = 𝒙+𝝅/𝟒
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2020 Boards

    CBSE Class 12 Sample Paper for 2019 Boards →
CBSE Class 12 Sample Paper for 2019 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo