Question
Download Solution PDFIf the value of tanθ + cotθ = √3, then find the value of tan6θ + cot6θ.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tanθ + cotθ = √3
Formula used:
(a + b)3 = a3 + b3 + 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
Calculation:
tanθ + cotθ = √3
Taking cube on both sides, we get
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
Taking square on the both sides
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ The value of tan6θ + cot6θ is - 2.
Last updated on Jun 2, 2025
-> The SSC Exam Dates 2025 has been released on the official website.
-> The SSC CGL Notification 2025 will be released on 9th June 2025 at ssc.gov.in.
-> The SSC CGL application 2025 submission will be open from 9th June to 4th July 2025.
-> The SSC CGL Tier 1 Exam 2025 Dates have been revised. The SSC CGL Exam will be conducted from 13 August to 30 August, 2025.
-> Candidates can refer to the SSC CGL syllabus for a better understanding of the exam structure and pattern.
-> The SSC CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.