

Get live Maths 1-on-1 Classs - Class 6 to 12
Miscellaneous
Misc. 2 Important
Misc. 3 Deleted for CBSE Board 2023 Exams
Misc. 4 Important Deleted for CBSE Board 2023 Exams
Misc. 5 Deleted for CBSE Board 2023 Exams
Misc. 6 Deleted for CBSE Board 2023 Exams
Misc. 7 Important Deleted for CBSE Board 2023 Exams
Misc. 8 Important Deleted for CBSE Board 2023 Exams
Misc. 9 Important Deleted for CBSE Board 2023 Exams
Misc. 10 Important Deleted for CBSE Board 2023 Exams
Misc. 11 Important Deleted for CBSE Board 2023 Exams
Misc 12 Important Deleted for CBSE Board 2023 Exams
Misc. 13 Important Deleted for CBSE Board 2023 Exams
Misc. 14 Deleted for CBSE Board 2023 Exams
Misc 15 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 16 (MCQ) Important Deleted for CBSE Board 2023 Exams
Misc 17 (MCQ) Deleted for CBSE Board 2023 Exams You are here
Miscellaneous
Last updated at March 30, 2023 by Teachoo
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)