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if, u=cot-1√tanx - tan-1√tanx then tan(pi/4-u/2) is |
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Answer» We know that \(tan^{-1}x+cot^{-1}x=\frac{\pi}{2}\) \(u=\frac{\pi}{2}-2tan^{-1}(\sqrt{tanx})\) \(2tan^{-1}x(\sqrt{tanx})=\frac{\pi}{2}-u\) \(tan^{-1}x(\sqrt{tanx})=\frac{\pi}{4}-\frac{u}{2}\) \(\sqrt{tanx}=tan(\frac{\pi}{4}-\frac{u}{2})\) |
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