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

Express sin^-1 ⁡( (sin⁡ x  + cos ⁡x)/ √2) in simplest form - Teachoo

Question 21 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2


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

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.