Solve the following equations for x:(i) tan−12x + tan−13x = nπ + 3π4(ii) tan−1(x + 1) + tan−1(x − 1) = tan−1831(iii) tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x(iv) tan−11-x1+x-12tan−1x = 0, where x > 0(v) cot−1x − cot−1(x + 2) = π12, x > 0(vi) tan−1(x + 2) + tan−1(x − 2) = tan−1879, x > 0(vii) tan-1x2+tan-1x3=π4, 0<x<6(viii) tan-1x-2x-4+tan-1x+2x+4=π4(ix) tan-12+x+tan-12-x=tan-123, where x<-3 or, x>3(x) tan-1x-2x-1+tan-1x+2x+1=π4

Solve the following equations for x:(i) tan−12x + tan−13x = nπ +

1.	Solve the following equations for x:(i) tan−12x + tan−13x = nπ + 3π4(ii) tan−1(x + 1) + tan−1(x − 1) = tan−1831(iii) tan−1(x −1) + tan−1x tan−1(x + 1) = tan−13x(iv) tan−11-x1+x-12tan−1x = 0, where x > 0(v) cot−1x − cot−1(x + 2) = π12, x > 0(vi) tan−1(x + 2) + tan−1(x − 2) = tan−1879, x > 0(vii) tan-1x2+tan-1x3=π4, 0<x<6(viii) tan-1x-2x-4+tan-1x+2x+4=π4(ix) tan-12+x+tan-12-x=tan-123, where x<-3 or, x>3(x) tan-1x-2x-1+tan-1x+2x+1=π4
Answer» Solve the following equations for x: (i) tan⁻¹2x + tan⁻¹3x = nπ + $\frac{3 π}{4}$ (ii) tan⁻¹(x + 1) + tan⁻¹(x − 1) = tan⁻¹ $\frac{8}{31}$ (iii) tan⁻¹(x −1) + tan⁻¹x tan⁻¹(x + 1) = tan⁻¹3x (iv) tan⁻¹ $(\frac{1 - x}{1 + x}) - \frac{1}{2}$ tan⁻¹x = 0, where x > 0 (v) cot⁻¹x − cot⁻¹(x + 2) = $\frac{π}{12}$ , x > 0 (vi) tan⁻¹(x + 2) + tan⁻¹(x − 2) = tan⁻¹ $(\frac{8}{79})$ , x > 0 (vii) $\tan^{- 1} \frac{x}{2} + \tan^{- 1} \frac{x}{3} = \frac{π}{4}, 0 < x < \sqrt{6}$ (viii) $\tan^{- 1} (\frac{x - 2}{x - 4}) + \tan^{- 1} (\frac{x + 2}{x + 4}) = \frac{π}{4}$ (ix) $\tan^{- 1} (2 + x) + \tan^{- 1} (2 - x) = \tan^{- 1} \frac{2}{3}, where x < - \sqrt{3} or, x > \sqrt{3}$ (x) $\tan^{- 1} \frac{x - 2}{x - 1} + \tan^{- 1} \frac{x + 2}{x + 1} = \frac{π}{4}$