Question
Download Solution PDFত্রিকোণমিতিক সূত্র ব্যবহার করে, \(\rm \left(\frac{\sin (x-y)}{\sin(x+y)}\right)\rm \left(\frac{\tan x+\tan y}{\tan x-\tan y}\right)\)এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFঅনুসৃত সূত্র:
Sin (A - B) = sin A × cos B - cos A × sin B
Sin (A + B) = sin A × cos B + cos A × sin B
গণনা:
\(\rm \left(\frac{\sin (x-y)}{\sin(x+y)}\right)\rm \left(\frac{\tan x+\tan y}{\tan x-\tan y}\right)\)
⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × {(sin x/cos x) + (sin y/cos y)}/{(sin x/cos x) + (sin y/cos y)}
⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × {(sin x × cos y) + (sin y × cos x/(cos x) × (cos y)}/{(sinx × cos y) + (sin y × cos x)/(cos x) × (cosy)}
⇒ (sin x × cos y - cos x × sin y)/(sin x × cos y + cos x × sin y) × (sin x × cos y) + (siny × cos x)/(sin x × cos y) + (sin y × cos x)
⇒ 1
∴ সঠিক উত্তর হল 1
Alternate Methodগণনা:
যদি আমরা x = 45°, এবং y = 0° রাখি তাহলে,
\(\rm \left(\frac{\sin (x-y)}{\sin(x+y)}\right)\rm \left(\frac{\tan x+\tan y}{\tan x-\tan y}\right)\)
⇒ sin (45 - 0)/sin(45 + 0) × {(tan 45 + tan 0)/(tan 45 - tan 0)}
⇒ sin 45/sin 45 × {(1 + 0)/(1 - 0)}
⇒ 1
∴ সঠিক উত্তর 1 হবে।
Last updated on Jul 19, 2025
-> The SSC CGL Notification 2025 has been announced for 14,582 vacancies of various Group B and C posts across central government departments.
-> CSIR NET City Intimation Slip 2025 has been released @csirnet.nta.ac.in.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025 in multiple shifts.
-> Aspirants should visit the official website @ssc.gov.in 2025 regularly for CGL Exam updates and latest announcements.
-> 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.