Question

If sin theta =5/13,find the value of 1+tan theta/1-tan theta

Answer 1

$(i \: put \: x \: in \: place \: of \: \theta \: for \: my \: convient) \\ \sin(x) = \frac{5}{13} \\ \cos(x) = \sqrt{1 - \sin {}^{2} (x) } \\ = \sqrt{1 - { (\frac{5}{13} )}^{2} } \\ = \sqrt{ \frac{{13 }^{2} - {5}^{2} }{ {13}^{2} } } \\ \cos(x) = \sqrt{ \frac{12 {}^{2} }{ {13}^{2} } } = \frac{12}{13 } \\ \tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ = \frac{ \: \frac{5}{13} \: }{ \frac{12}{13} } = \frac{5}{12}$

$\frac{1 + \tan(x) }{1 - \tan(x) } \\ = \ \frac{1 + \frac{5}{12} }{1 - \frac{ 5 }{12} } \\ = \frac{ \: \: \: \: \frac{12 + 5}{12} \: \: \: \: }{ \frac{12 - 5}{12} } = \frac{17}{7}$