If sec theta tan theta sec theta minus tan theta 5 3 then sin theta is ........

Quantitative Aptitude ( CCS) Trignometry

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If (secθ+tanθ)/(secθ−tanθ)=5/3 then sinθ is,

1/2

1/3

1/4

1/5

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Explanation:

As usual detecting the possibility of taking out secθ as a factor from both numerator and denominator we take up the transformation,
(secθ+tanθ)/(secθ−tanθ)=5/3,
Or, secθ(1+sinθ)/secθ(1−sinθ)=53,
Or, (1+sinθ)/(1−sinθ)=5/3.
This is ripe form for applying the Componendo dividendo technique. We thus get,
sinθ=(5−3)/(5+3)=1/4