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 Jul 22, 2025
-> The SSC CGL Notification 2025 has been announced for 14,582 vacancies of various Group B and C posts across central government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025 in multiple shifts.
-> Candidates had filled out the SSC CGL Application Form from 9 June to 5 July, 2025. Now, 20 lakh+ candidates will be writing the SSC CGL 2025 Exam on the scheduled exam date. Download SSC Calendar 2025-25!
-> In the SSC CGL 2025 Notification, vacancies for two new posts, namely, "Section Head" and "Office Superintendent" have been announced.
-> 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, with the age limit varying from post to post.
-> The SSC CGL Salary structure varies by post, with entry-level posts starting at Pay Level-4 (Rs. 25,500 to 81,100/-) and going up to Pay Level-7 (Rs. 44,900 to 1,42,400/-).
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.