Search for: If ∫1a2sin2x+b2cos2x−dx=112tan−1(3tanx)+C, then the maximum value of a sin x + b cos x, isIf ∫1a2sin2x+b2cos2x−dx=112tan−1(3tanx)+C, then the maximum value of a sin x + b cos x, isA41B40C39D38 Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:We have, I=∫1a2sin2x+b2cos2xdx⇒ I=∫sec2xb2+a2tan2xdx⇒ I=1a∫1b2+(atanx)2d(atanx) =1abtan−1abtanx+C∴ ab=12 and ab=3⇒a2=36⇒a=±6∴ ab=12⇒b=±2Thus, we have asinx+bcosx=±(6sinx+2cosx)We know that −a2+b2≤asinx+bcosx≤a2+b2 for all x∴ −40≤±6sinx±2cosx≤40 for all x.Post navigationPrevious: The integral ∫0π1+4sin2x2-4sinx2 dx equalsNext: The value of ∫−11 xd|x|, isRelated content JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria JEE 2024: Exam Date, Syllabus, Eligibility Criteria NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3 JEE Crash Course – JEE Crash Course 2023 NEET Crash Course – NEET Crash Course 2023 JEE Advanced Crash Course – JEE Advanced Crash Course 2023