Solve the following equations for x:(i) tan-114+2 tan-115+tan-116+tan-11x=π4(ii) 3 sin-12x1+x2-4 cos-11-x21+x2+2 tan-12x1-x2=π3(iii) tan-12x1-x2+cot-11-x22x=2π3, x>0(iv) 2 tan-1 (sinx) =tan-1 (2 sinx), x≠π2.(v)cos-1x2-1x2+1+12tan-12x1-x2=2π3(vi) tan-1 x-2x-1+tan-1 x+2x+1=π4

Solve the following equations for x:(i) tan-114+2 tan-115+tan-116+tan-

1.	Solve the following equations for x:(i) tan-114+2 tan-115+tan-116+tan-11x=π4(ii) 3 sin-12x1+x2-4 cos-11-x21+x2+2 tan-12x1-x2=π3(iii) tan-12x1-x2+cot-11-x22x=2π3, x>0(iv) 2 tan-1 (sinx) =tan-1 (2 sinx), x≠π2.(v)cos-1x2-1x2+1+12tan-12x1-x2=2π3(vi) tan-1 x-2x-1+tan-1 x+2x+1=π4
Answer» Solve the following equations for x: (i) $\tan^{- 1} \frac{1}{4} + 2 \tan^{- 1} \frac{1}{5} + \tan^{- 1} \frac{1}{6} + \tan^{- 1} \frac{1}{x} = \frac{π}{4}$ (ii) $3 \sin^{- 1} \frac{2 x}{1 + x^{2}} - 4 \cos^{- 1} \frac{1 - x^{2}}{1 + x^{2}} + 2 \tan^{- 1} \frac{2 x}{1 - x^{2}} = \frac{π}{3}$ (iii) $\tan^{- 1} (\frac{2 x}{1 - x^{2}}) + \cot^{- 1} (\frac{1 - x^{2}}{2 x}) = \frac{2 π}{3}, x > 0$ (iv) 2 $\tan^{- 1}$ ( $\sin$ $x$ ) $=$ $\tan$ ^{$-$ 1} (2 $\sin$ $x$ ), $x \neq \frac{π}{2}$ . (v) $\cos^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + \frac{1}{2} \tan^{- 1} (\frac{2 x}{1 - x^{2}}) = \frac{2 π}{3}$ (vi) $\tan^{- 1} (\frac{x - 2}{x - 1}) + \tan^{- 1} (\frac{x + 2}{x + 1}) = \frac{π}{4}$