Question
Download Solution PDFযদি \(tan40^0 = \alpha\) , তবে \(\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}\) খুঁজে বের করো।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
tan 40° = α
ব্যবহৃত সূত্র:
tan (A - B) = (tan A - tan B)/1 + tan A × tan B
tan (90° - θ) = cot θ
cot θ × tan θ = 1
গণনা:
⇒ \(\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}\) = tan (320° - 310°)
⇒ tan 10°
এখন, আমরা লিখতে পারি:
Tan 10° = tan (50° - 40°)
⇒ [(tan 50° - tan 40°)/1 + (tan 50° × tan 40°)]
⇒ [tan (90° - 40°) - tan 40°/1 + tan (90° - 40°) × tan 40°]
⇒ cot 40° - tan 40°/1 + cot 40° × tan 40°
⇒ (1/α - α)/1 + 1
⇒ (1/α - α)/2
⇒ (1 - α2)/2α
∴ সঠিক উত্তর হল (1 - α2)/2α.
Last updated on Jul 22, 2025
-> The IB Security Assistant Executive Notification 2025 has been released on 22nd July 2025 on the official website.
-> 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.
-> 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.