Question
Download Solution PDFIf 4 tan-1 x + cot‑1 x = π, then x equals:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\(\rm \cot \theta = \tan \left(\dfrac{\pi}{2}-\theta\right)\).
\(\tan^{-1} x = \dfrac{\pi}{2}-\cot^{-1} x\)
Calculation:
4 tan-1 x + cot‑1 x = π
\( 4\tan^{-1}x+\left(\dfrac{\pi}{2}-\tan^{-1}x\right)=\pi\)
\(3\tan^{-1}x=\pi-\dfrac{\pi}{2}=\dfrac{\pi}{2}\)
\( \tan^{-1}x=\dfrac{\pi}{6}\)
\(x=\tan\dfrac{\pi}{6}=\dfrac{1}{\sqrt3}\).
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.