If P cos α = 3 and 4 tan α = Q, then what is the relation between P and Q, which is independent of α?  

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 2)
View all SSC CGL Papers >
  1. \(\rm \frac{9}{p^2}+\frac{16}{Q^2}=1\)
  2. \(\rm \frac{9}{p^2}-\frac{16}{Q^2}=1\)
  3. \(\rm \frac{p^2}{9}-\frac{Q^2}{16}=1\)
  4. \(\rm \frac{p^2}{9}+\frac{Q^2}{16}=1\)

Answer (Detailed Solution Below)

Option 3 : \(\rm \frac{p^2}{9}-\frac{Q^2}{16}=1\)
ssc-cgl-offline-mock
Free
SSC CGL Tier 1 2025 Full Test - 01
3.8 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Concept used:

sec2 θ - tan2 θ = 1

Calculation:

P cos α = 3

⇒ cos α = 3/P

⇒ sec α = P/3

4 tan α = Q

⇒ tan α = Q/4

From the given concept, we get

sec2 α - tan2 α = 1

⇒ P2/9 - Q2/16 = 1

∴ The correct answer is option 3

Latest SSC CGL Updates

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.

Get Free Access Now
Hot Links: teen patti boss teen patti vip teen patti master online teen patti dhani teen patti master king