If $21 tan θ = 20,$ then $(1+ sinθ - cosθ) : ( 1 - sin θ + cos θ) $ is equal to :

14 : 15

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