Question

If 3 tan A = 4, then find sin A and cos A​

Answer 1

$3tan \alpha = 4 \\ tan \alpha = \frac{4}{3} \\ sec \alpha = \sqrt{1 + {tan}^{2} \alpha } \\ = \sqrt{1 + \frac{16}{9} } \\ = \sqrt{ \frac{25}{9} } \\ = \frac{5}{3} \\ cos \alpha = \frac{1}{sec \alpha } = \frac{3}{5} \\ sin \alpha = \sqrt{1 - {cos}^{2} \alpha } \\ = \sqrt{1 - \frac{9}{25} } \\ = \sqrt{ \frac{16}{25} } \\ = \frac{4}{5}$