Saved Bookmarks
| 1. |
\( \operatorname{5tan}^{-1}(x)+3 \cot ^{-1}(x)=\frac{7 \pi}{4} \) |
|
Answer» 5 tan-1x + 3 cot-1x = \(\frac{7\pi}4\) ⇒ 2 tan-1x + 3(tan-1x + cot-1x) = \(\frac{7\pi}4\) ⇒ 2 tan-1x + \(\frac{3\pi}2\) = \(\frac{7\pi}4\) ⇒ 2 tan-1x = \(\frac{7\pi}4\) - \(\frac{3\pi}2\) = \(\frac{7\pi-5\pi}4=\frac{\pi}4\) ⇒ tan-1x = \(\frac{\pi}8\) ⇒ x = tan\((\frac{\pi}8)\) ≅ 0.414 |
|