If $21 \tan \theta = 20$, then $(1 + \sin \theta + \cos \theta) : (1 - \sin \theta + \cos \theta) = ?$

7 : 3

21 tanθ = 20

{ using , tanθ = \(\frac{P}{B}\) }

tanθ = \(\frac{20}{21}\)

By using pythagoras theorem ,

P² + B² = H²

20² + 21² = H²

H = 29

Now,

( 1 + sinθ + cosθ ) : ( 1 - sinθ + cosθ ) 

( 1 + \(\frac{P}{H}\) + \(\frac{B}{H}\) ) : ( 1 - \(\frac{P}{H}\) + \(\frac{B}{H}\) )

( 1 + \(\frac{20}{29}\) + \(\frac{21}{29}\) ) : ( 1 - \(\frac{20}{29}\) + \(\frac{21}{29}\) )

( 29 + 20 + 21 )  :  ( 29 - 20 + 21 )

70 :  30

 7  :   3