If \(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{4}{5}\), find sinθ .
Answer & explanation
Correct answer: option 4
\(\frac{secθ - tanθ}{secθ + tanθ}\) = \(\frac{4}{5}\)
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)