If $21 tan θ = 20,$ then $(1+ sinθ - cosθ) : ( 1 - sin θ + cos θ) $ is equal to :
Answer & explanation
Correct answer: option 3
21 tan θ = 20
tan θ = \(\frac{20}{21}\)
{ tan θ = \(\frac{P}{B}\) }
By using pythagoras theorem,
P² + B² = H²
20² + 21² = H²
H = 29
Now,
( 1 + sinθ - cosθ ) : ( 1 - sinθ + cosθ )
( 1 + \(\frac{20}{29}\) - \(\frac{21}{29}\) ) : ( 1 - \(\frac{20}{29}\) + \(\frac{21}{29}\) )
( \(\frac{29 + 20 - 21 }{29}\) ) : ( \(\frac{29 - 20 + 21 }{29}\) )
( \(\frac{28 }{29}\) ) : ( \(\frac{30 }{29}\) )
14 : 15