If \(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{4}{5}\), find sinθ .

\(\frac{1}{9}\)

\(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{4}{5}\)

By componendo & Dividendo concept:

\(\frac{secθ}{tanθ}\) = \(\frac{5 + 4}{5 - 4}\)

\(\frac{\frac{1}{cos}}{\frac{sin}{cos}}\) = \(\frac{9}{1}\)

\(\frac{1}{sinθ}\) = \(\frac{9}{1}\)

⇒ sinθ = \(\frac{1}{9}\)   (where 1 → P and 9 → H)