If \(\frac{sec θ + tan θ}{sec θ - tan θ}\) = 2\(\frac{31}{49}\) ; then value of sin θ is?
Answer & explanation
Correct answer: option 3
\(\frac{sec θ + tan θ}{sec θ - tan θ}\) = 2\(\frac{31}{49}\)
⇒ \(\frac{ 1+ sin θ}{ 1 - sin θ}\) = \(\frac{129}{49}\)
⇒ 49 ( 1 + sin θ ) = 129 ( 1 - sin θ )
⇒ 49 + 49 sin θ = 129 - 129 sin θ
⇒ 129 sin θ + 49 sin θ = 129 - 49
⇒ 178 sin θ = 80
⇒ sin θ = \(\frac{80}{178}\) = \(\frac{40}{89}\)