Question
Download Solution PDFComprehension
Consider the following for the two (02) items that follow:
Let the function y = (1 - cos x)-1 where\(x \ne 2n\pi\) and n is an integer
What is the range of the function?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
The function is\(y = \left( 1 - \cos(x) \right)^{-1} \), where \(x \neq 2n\pi \)and n is an integer.
The cosine function has a range of [-1, 1] , so cos(x) can take values from ( -1) to ( 1 ).
The expression \(1 - \cos(x) \) will take values from:
\( 1 - 1 = 0 \quad \text{to} \quad 1 - (-1) = 2 \)
So, (1 - cos(x)) takes values in the range \((0, 2] \), but \(x \neq 2n\pi \) excludes the value 0.
Since \(y = \frac{1}{1 - \cos(x)} \), the reciprocal function will take values in the range \(\left[ \frac{1}{2}, \infty \right) \)
∴ The range of the function is \([0.5, \infty) \).
The correct answer is Option (b)
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> 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.