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sin theta = 5/3
sin theta = perpendicular/ hypotenuse
sin theta= 5/3
perpendicular/ hypotenuse= 5/3
now perpendicular= 5 unit, hypotenuse= 3 unit
now in right angled triangle ABC
(Hypotenuse)^ 2= ( perpendicular)^2 + ( base )^2
(3)^2=(5)^2+ ( base)^ 2
9=25+ base^2
base^ 2= 25-9
base^2= 16
base=√ 16= 4 unit
base.= 4unit
sec theta = hypotenuse/ base
sec theta = 3/4
tan theta =perpendicular/ base
tan theta = 5/4
so sec theta + tan theta = 3/4+5/4=3+5/4=8/4=2
and sec theta -tan theta= 3/4 -5/4=3 - 5/4=-2/4
=-1/2
now sec theta + tan theta/ sec. theta- tan theta
2/-1/2= 2×2/-1 =-4
I hope this will help
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