Search for: Let α,β be the roots of x2−2xcosϕ+1=0 then the equation whose roots are αn and βn isLet α,β be the roots of x2−2xcosϕ+1=0 then the equation whose roots are αn and βn isAx2−2xcosnϕ−1=0Bx2−2xcosnϕ+1=0Cx2−2xsinnϕ+1=0Dx2+2xsinnϕ−1=0 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:The given equation is x2−2xcosϕ+1=0∴ x=2cosϕ±4cos2ϕ−42=cosϕ±isinϕ Let α=cosϕ+isinϕ, then β=cosϕ−isinϕ ∴ αn+βn=(cosϕ+isinϕ)n+(cosϕ−isinϕ)n =2cosnϕ and αnβn=(cosnϕ+isinnϕ)(cosnϕ−isinnϕ)=cos2nϕ+sin2nϕ=1∴ Required equation isx2−2xcosnϕ+1=0Post navigationPrevious: ∫xsin−1xdx is equal to Next: lf a, b and c are the sides of △ABC such that a≠b≠c and x2−2(a+b+c)x+3λ (ab+bc+ca)=0 has real roots, thenRelated content 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 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