If \(\frac{sec θ + tan θ}{sec θ - tan θ}\) = 2\(\frac{22}{31}\); then value of sin θ is?
Answer & explanation
Correct answer: option 3
\(\frac{sec θ + tan θ}{sec θ - tan θ}\) = 2\(\frac{22}{31}\)
⇒ \(\frac{ 1+ sin θ}{ 1 - sin θ}\) = \(\frac{84}{31}\)
⇒ 31 ( 1 + sin θ ) = 84 ( 1 - sin θ )
⇒ 31 + 31 sin θ = 84 - 84 sin θ
⇒ 84 sin θ + 31 sin θ = 84 - 31
⇒ 115 sin θ = 53
⇒ sin θ = \(\frac{53}{115}\)