If 5sinθ - 12cosθ = 0
find the value of \(\frac{1+sinθ+cosθ}{1-sinθ+cosθ}\).
Answer & explanation
Correct answer: option 2
5sinθ - 12cosθ = 0
5sinθ = 12cosθ
\(\frac{sinθ}{cosθ}\) = \(\frac{12}{5}\)
tanθ = \(\frac{12}{5}\) = \(\frac{P}{B}\) [Triplet 5, 12, 13]
P = 12, B = 5, H = 13,
⇒ sinθ = \(\frac{P}{H}\) = \(\frac{12}{13}\), and
⇒ cosθ = \(\frac{B}{H}\) = \(\frac{5}{13}\)
Now,
⇒ \(\frac{1\;+\;sinθ\;+\;cosθ}{1\;-\;sinθ\;+\;cosθ}\) = \(\frac{1\;+\;\frac{12}{13}\;+\;\frac{5}{13}}{1\;-\;\frac{12}{13}\;+\;\frac{5}{13}}\) = \(\frac{30}{20}\) = \(\frac{3}{2}\)