Question

if sin theta=3/5 find the value of tan theta + cot theta/ tan theta-cot theta​

Answer 1

Step-by-step explanation:

$sinΘ = \frac{3}{5} \\ \\ cosΘ = \sqrt{1 - {sin}^{2}Θ } \\ = \sqrt{1 - {( \frac{3}{5} )}^{2} } \\ = \sqrt{1 - \frac{9}{25} } \\ = \sqrt{ \frac{16}{25} } \\ = \frac{4}{5} \\ \\ tanΘ = \frac{sinΘ}{cosΘ} = \frac{3}{5} \times \frac{5}{4} = \frac{3}{4} \\ \\ cot Θ = \frac{4}{3} \\ \\ = \frac{tan Θ + cotΘ\: }{tanΘ - cotΘ} \\ \\ = \frac{ \frac{3}{4} + \frac{4}{3} }{ \frac{3}{4} - \frac{4}{3} } \\ \\ = \frac{ \frac{25}{12} }{ - \frac{7}{12} } \\ \\ = - \frac{25}{7}$