If 5 sinθ = 7 cosθ . Then find the value of cosecθ .

\(\frac{3}{7}\)  \(\frac{\sqrt {74}}{7}\)  \(\frac{\sqrt {75}}{7}\)  \(\frac{\sqrt {74}}{15}\)

\(\frac{\sqrt {74}}{7}\)

5 sinθ = 7 cosθ tanθ = \(\frac{7}{5}\)  (where 7 → P and 5 → B) H = \(\sqrt {(7)^2 + (5)^2}\) H = \(\sqrt {49 + 25}\) = \(\sqrt {74}\) cosecθ = \(\frac{H}{P}\) =  \(\frac{\sqrt {74}}{7}\)