If \(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{3}{4}\), find sinθ .

\(\frac{1}{7}\)

\(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{3}{4}\)

By componendo & Dividendo concept:

\(\frac{secθ}{tanθ}\) = \(\frac{4 + 3}{4 - 3}\)

\(\frac{\frac{1}{cos}}{\frac{sin}{cos}}\) = \(\frac{7}{1}\)

\(\frac{1}{sinθ}\) = \(\frac{7}{1}\)

⇒ sinθ = \(\frac{1}{7}\)   (where 1 → P and 7 → H)