(i) 2sin-135=tan-1247(ii) tan-114+tan-129=12cos-135=12sin-145(iii) tan-123=12tan-1125(iv) tan-117+2 tan-113=π4(v) sin-145+2 tan-113=π2(vi) 2 sin-135-tan-11731=π4(vii) 2 tan-115+tan-118=tan-147(viii) 2 tan-134-tan-11731=π4(ix) 2 tan-112+tan-117=tan-13117(x) 4tan-115-tan-1 1239=π4

(i) 2sin-135=tan-1247(ii) tan-114+tan-129=12cos-135=12sin-145(iii) t

1.	(i) 2sin-135=tan-1247(ii) tan-114+tan-129=12cos-135=12sin-145(iii) tan-123=12tan-1125(iv) tan-117+2 tan-113=π4(v) sin-145+2 tan-113=π2(vi) 2 sin-135-tan-11731=π4(vii) 2 tan-115+tan-118=tan-147(viii) 2 tan-134-tan-11731=π4(ix) 2 tan-112+tan-117=tan-13117(x) 4tan-115-tan-1 1239=π4
Answer» (i) $2 \sin^{- 1} \frac{3}{5} = \tan^{- 1} \frac{24}{7}$ (ii) $\tan^{- 1} \frac{1}{4} + \tan^{- 1} \frac{2}{9} = \frac{1}{2} \cos^{- 1} \frac{3}{5} = \frac{1}{2} \sin^{- 1} (\frac{4}{5})$ (iii) $\tan^{- 1} \frac{2}{3} = \frac{1}{2} \tan^{- 1} \frac{12}{5}$ (iv) $\tan^{- 1} \frac{1}{7} + 2 \tan^{- 1} \frac{1}{3} = \frac{π}{4}$ (v) $\sin^{- 1} \frac{4}{5} + 2 \tan^{- 1} \frac{1}{3} = \frac{π}{2}$ (vi) $2 \sin^{- 1} \frac{3}{5} - \tan^{- 1} \frac{17}{31} = \frac{π}{4}$ (vii) $2 \tan^{- 1} \frac{1}{5} + \tan^{- 1} \frac{1}{8} = \tan^{- 1} \frac{4}{7}$ (viii) $2 \tan^{- 1} \frac{3}{4} - \tan^{- 1} \frac{17}{31} = \frac{π}{4}$ (ix) $2 \tan^{- 1} (\frac{1}{2}) + \tan^{- 1} (\frac{1}{7}) = \tan^{- 1} (\frac{31}{17})$ (x) $4 \tan^{- 1} \frac{1}{5} - \tan^{- 1} \frac{1}{239} = \frac{π}{4}$