Search for: If x cos α+y sin α=x cos β+y sin β=2a, then cos α cos β is,If x cos α+y sin α=x cos β+y sin β=2a, then cos α cos β is,A4axx2+y2B4a2−y2x2+y2C4ayx2+y2D4a2−x2x2+y2 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,xcosα+ysinα=xcosβ+ysinβ=2a⇒ α,β are the roots of x cosθ+y sinθ=2a. Now, xcosθ+ysinθ=2a⇒(xcosθ−2a)2=y2sin2θ⇒x2cos2θ−4axcosθ+4a2=y21−cos2θ⇒x2+y2cos2θ−4axcosθ+4a2−y2=0Clearly, cos α,cos β are the roots of this equation. ∴ cosαcosβ=4a2−y2x2+y2.Post navigationPrevious: The value of sin8 θ+cos8 θ+sin6 θcos2 θ +3 sin4 θcos2 θ+cos6 θsin2 θ+3 sin2 θcos4 θ is equal toNext: In a △ABC, if A=45∘ and C=60∘ then a+2c=Related content JEE Main 2023 Result: Session 1 NEET 2024 JEE Advanced 2023 NEET Rank Assurance Program | NEET Crash Course 2023 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