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Find the value of sin-1 (cos x), x∈ [-π/2, π/2]

  1. x
  2. π - x
  3. \(\rm \left(\frac {\pi}{2} - x\right)\)
  4. -x

Answer (Detailed Solution Below)

Option 3 : \(\rm \left(\frac {\pi}{2} - x\right)\)
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Detailed Solution

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Concept:

sin-1 (sin x) = x

 

Calculation

Given: x∈ [-π/2, π/2] 
sin-1 (cos x) = sin-1 sin \(\rm \left(\frac {\pi}{2} - x\right)\)
As we know that, sin-1 (sin x) = x
Therefore,sin-1 (cos x) = sin-1 sin \(\rm \left(\frac {\pi}{2} - x\right)\) = \(\rm \left(\frac {\pi}{2} - x\right)\) 
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Last updated on Jul 1, 2025

-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).

->The Exam will be held on 9th July 2025.

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

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