Question

If cosec A + cot A =11/2, then tan A is ? I need the answer not any foolish reply​

Answer 1

$= > cosecx + cotx = \frac{11}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)\\ \\ = > {cosec}^{2} = 1 + {cot}^{2}x \\ = > {cosec}^{2} - {cot}^{2} x = 1 \\ = > (cosecx + cotx)(cosecx - cotx) = 1 \\ = > \frac{11}{2} (cosecx - cotx) = 1 \: \: \: \: \: \: ... \: (from \: i) \\ = > cosecx - cotx = \frac{2}{11} \\ mutiplying \: by \: - 1 \: throughout \\ = > - cosecx + cotx = - \frac{2}{11} \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (ii) \\ \\ adding \: (i) \: and \:( ii) \\ \\ \: \: \: \: \: \: \: \: \: \: \: cosecx \: + \: cotx = \frac{11}{2} \\ (+) - cosecx + cotx = - \frac{2}{11} \\ - - - - - - - - - - - - - - - - - \\ 0 + 2cotx = \frac{11}{2} - \frac{2}{11} \\ = > 2cotx = \frac{121 - 4}{22} \\ = > cotx = \frac{117}{44} \\ \\ since \: tanx = \frac{1}{cotx} \\ hence \\ tanx = \frac{44}{117}$

Hence, tanx = 44/117.