Question
Download Solution PDFIf tan A + cot A = 2, then the value of 2(tan2 A + cot2 A) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
tan A + cot A = 2
Calculation:
According to the question,
we have tan A + cot A = 2
Squaring both sides, we get
⇒ (tan A + cot A)2 = (2)2
⇒ tan2 A + cot2 A + 2(tan A)(cot A) = 4
⇒ tan2 A + cot2 A + 2(tan A)(1/tan A) = 4
⇒ tan2 A + cot2 A + 2 = 4
⇒ tan2 A + cot2 A = 2
Now,
2(tan2 A + cot2 A) = 2 × 2
⇒ 4
∴ The value of 2(tan2 A + cot2 A) is 4.
Shortcut Trick We can go with the value-putting method,
If we put A = 45° it satisfies the equation tan A + cot A = 2, so
2(tan2 A + cot2 A)
⇒ 2(1 + 1)
⇒ 4
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The 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.