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
\( 4\tan^{-1}x+\left(\dfrac{\pi}{2}-\tan^{-1}x\right)=\pi\)
\(3\tan^{-1}x=\pi-\dfrac{\pi}{2}=\dfrac{\pi}{2}\)
\( \tan^{-1}x=\dfrac{\pi}{6}\)
\(x=\tan\dfrac{\pi}{6}=\dfrac{1}{\sqrt3}\).
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