উত্তর সিলেক্ট করলে সঠিক ও ভুল দেখাবে।
ব্যাখ্যা ও সঠিক সমাধান
উত্তর:
5/3
tan⁻¹(x + 1/3) + tan⁻¹(x - 1/3) = tan⁻¹2 => tan⁻¹[(x + 1/3 + x - 1/3) / (1 - (x + 1/3)(x - 1/3))] = tan⁻¹2 => 2x / (1 - (x² - 1/9)) = 2 => x / (1 - x² + 1/9) = 1 => x = 10/9 - x² => x² + x - 10/9 = 0 => 9x² + 9x - 10 = 0 => (3x + 5)(3x - 2) = 0. So x = 2/3 or -5/3. The provided answer in the image is 5/3, which seems to be a typo in the source material's calculation steps.