Question

what is the answer ​

Answer 1

Answer:

Here is the answer.

Step-by-step explanation:

Given,

$sin\theta = \frac{5}{13} \\ we \: know \\ cos\theta = \sqrt{1 - {sin}^{2}\theta } \\ = > cos\theta = \sqrt{1 - {( \frac{5}{13}) }^{2} } \\ = > cos\theta = \sqrt{1 - \frac{25}{169} } \\ = > cos\theta = \sqrt{ \frac{169 - 25}{169} } \\ = > cos\theta = \sqrt{ \frac{144}{169} } \\ = > cos\theta = \frac{12}{13} \\ \\ \therefore \: tan\theta + \frac{1}{cos\theta} \\ = \frac{sin\theta}{cos\theta} + \frac{1}{cos\theta} \\ = \frac{( \frac{5}{13}) }{( \frac{12}{13} )} + \frac{1}{( \frac{12}{13}) } \\ = \frac{5}{13} \times \frac{13}{12} + \frac{13}{12} \\ = \frac{5}{12} + \frac{13}{12} \\ = \frac{5 + 13}{12} \\ = \frac{18}{12} \\ = \frac{3}{2}$