If 4 sin-1 x + cos-1 x = π, then what is sin-1 x + 4 cos-1 x equal to?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
View all NDA Papers >
  1. π/2
  2. π 
  3. 3π/2
  4. 2π 

Answer (Detailed Solution Below)

Option 3 : 3π/2
Free
NDA 01/2025: English Subject Test
5.3 K Users
30 Questions 120 Marks 30 Mins

Detailed Solution

Download Solution PDF

Explanation:

Given:

4 sin-1 x + cos-1 x = π 

⇒ \(4( \frac{\pi }{2} - Cos^{-1}x) + (\frac{\pi }{2} - sin^{-1}x) = \pi \)

⇒ \(2\pi - 4cos^{-1}x + \frac{\pi }{2} - sin^{-1}x = \pi \)

⇒ 4cos-1 x + sin-1x = \(\frac{3\pi}{2}\)

∴ Option (c) is correct

Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Get Free Access Now
Hot Links: real teen patti teen patti refer earn teen patti customer care number teen patti noble