Question

help me to solve this ​

Answer 1

Step-by-step explanation:

$13sin \: \theta \: = 5 \\ sin \: \theta \: = \frac{5}{13} \\ cos \: \theta = \sqrt{1 - {sin}^{2} \theta} \\ = \sqrt{1 - (\frac{5}{13})^{2} } = \sqrt{1 - \frac{25}{169} } \\ = \sqrt{ \frac{169 - 25}{169} } = \sqrt{ \frac{144}{196} } \\ cos \: \theta = \frac{12}{13} \\ tan \: \theta \: = \frac{sin \theta}{cos \theta} = \frac{ \frac{5}{13} }{ \frac{12}{13} } = \frac{5}{12} \\ \frac{5sin \theta - 2cos \theta}{tan \theta} = \frac{5 \times \frac{5}{13} - 2 \times \frac{12}{13} }{ \frac{5}{12} } \\ = \frac{ \frac{25}{13 } - \frac{24}{13} }{ \frac{5}{12} } = \frac{ \frac{25 - 24}{13} }{ \frac{5}{12} } = \frac{ \frac{1}{13} }{ \frac{5}{12} } \\ = \frac{1}{13} \times \frac{12}{5} \\ = \frac{12}{65} \\ thus \\ \frac{5sin \theta - 2cos \theta}{tan \theta} = \frac{12}{65}$