If \(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{3}{5}\), find (\(\frac{cosecθ + cotθ}{cosecθ - cotθ}\)).
Answer & explanation
Correct answer: option 2
\(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{3}{5}\)
By componendo & Dividendo concept:
\(\frac{secθ}{tanθ}\) = \(\frac{5 + 3}{5 - 3}\)
\(\frac{\frac{1}{cos}}{\frac{sin}{cos}}\) = \(\frac{8}{2}\)
\(\frac{1}{sinθ}\) = \(\frac{4}{1}\)
⇒ sinθ = \(\frac{1}{4}\) (where 1 → P and 4 → H)
⇒ cosecθ = 4
So, Base = \(\sqrt {(4)^2 - (1)^2}\) = \(\sqrt {15}\),
⇒ cotθ= \(\frac{\sqrt {15}}{1}\) = \(\sqrt {15}\)
Put the values and find:
⇒ \(\frac{cosecθ + cotθ}{cosecθ - cotθ}\) = \(\frac{4 + \sqrt {15}}{4 - \sqrt {15}}\) = 31 + 8\(\sqrt {15}\)