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Last updated at Aug. 11, 2021 by Teachoo

Transcript

Misc 17 Solve tan−1 (x/y) – tan−1 (x − y)/(x + y) is equal to (A) π/2 (B) π/3 (C) π/4 (D) (−3π)/4 We know that tan–1 x – tan–1 y = tan–1 ((𝐱 − 𝐲)/(𝟏 + 𝐱𝐲)) tan−1 x/y – tan−1 ((x − y)/(x + y)) = tan−1 [(x/y − (x − y )/(x + y))/(1 + (x/y) ((x − y )/(x + y)) )] Replacing x by 𝑥/𝑦 & y by (x − y)/(x + y) = tan−1 (((𝑥 ( 𝑥 + 𝑦 ) − 𝑦 ( 𝑥 − 𝑦 ))/(𝑦 ( 𝑥 + 𝑦 ) ))/((𝑦 ( 𝑥 + 𝑦 )+ 𝑥 ( 𝑥 − 𝑦))/(𝑦 ( 𝑥 + 𝑦) ))) = tan−1 ((𝑥 ( 𝑥 + 𝑦 ) − 𝑦 ( 𝑥 − 𝑦 ))/(𝑦 ( 𝑥 + 𝑦 ) ) × (𝑦 (𝑥 + 𝑦))/(𝑦 ( 𝑥 + 𝑦 )+ 𝑥 ( 𝑥 −𝑦) )) = tan−1 ((𝑥 ( 𝑥 + 𝑦 ) − 𝑦 ( 𝑥 − 𝑦 ))/(𝑦 ( 𝑥 + 𝑦 ) + 𝑥 (𝑥 + 𝑦)) × (𝑦 (𝑥 + 𝑦))/(𝑦 (𝑥 + 𝑦) )) = tan−1 ((𝑥 ( 𝑥 + 𝑦 ) − 𝑦 ( 𝑥 − 𝑦 ))/(𝑦 ( 𝑥 + 𝑦 ) + 𝑥 (𝑥 + 𝑦))) = tan−1 ((𝑥2+ 𝑥𝑦 − 𝑦𝑥 + 𝑦2)/(𝑦𝑥 +𝑦2 + 𝑥2 − 𝑥𝑦))) = tan−1 ((𝑥2+ 𝑦2+ 𝑦𝑥 − 𝑦𝑥)/(𝑦2 + 𝑥2 + 𝑦𝑥 − 𝑥𝑦))) = tan−1 ((𝑥2+ 𝑦2 )/(𝑦2 + 𝑥2 )) = tan−1 (1) = tan−1 ("tan " π/4) = π/4 Hence, Correct answer is C (As tan 𝜋/4 = 1)

Formulae based

Inverse Trigonometry Formulas

Example 3 (i) Important

Ex 2.2,1 Deleted for CBSE Board 2022 Exams

Ex 2.2, 2 Important Deleted for CBSE Board 2022 Exams

Example 8 Deleted for CBSE Board 2022 Exams

Ex 2.2, 12 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 14 Important Deleted for CBSE Board 2022 Exams

Example 4 Deleted for CBSE Board 2022 Exams

Ex 2.2, 3 Deleted for CBSE Board 2022 Exams

Misc. 8 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 4 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 15 Important Deleted for CBSE Board 2022 Exams

Example 13 Important Deleted for CBSE Board 2022 Exams

Misc. 14 Deleted for CBSE Board 2022 Exams

Misc 17 (MCQ) Deleted for CBSE Board 2022 Exams You are here

Misc. 13 Important Deleted for CBSE Board 2022 Exams

Example 10 Important Deleted for CBSE Board 2022 Exams

Misc. 3 Deleted for CBSE Board 2022 Exams

Misc. 4 Important Deleted for CBSE Board 2022 Exams

Misc 12 Important Deleted for CBSE Board 2022 Exams

Misc 16 (MCQ) Important Deleted for CBSE Board 2022 Exams

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.