Question

if seca =5/4,then find the value of 1-tana/1+tana​

Answer 1

Answer:

$1 + { \tan }^{2} a = { \sec}^{2} a \\ { \tan}^{2} = { \sec }^{2} a - 1 \\ { \tan }^{2} a = \frac{ {5}^{2} }{ {4}^{2} } - 1 \\ { \tan }^{2} a = \frac{25}{16} - 1 \\ { \tan}^{2} a = \frac{25 - 16}{16} \\ { \tan}^{2} a = \frac{9}{25} \\ \tan(a) = \frac{3}{5}$

$\frac{1 - \tan(a) }{1 + \tan(a) } \\ = \frac{1 - \frac{3}{5} }{1 + \frac{3}{5} } \\ = \frac{ \frac{5 - 3}{5} }{ \frac{5 + 3}{5} } \\ = \frac{5 - 3}{5 + 3} \\ = \frac{2}{8} \\ = \frac{1}{4}$

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