If $\;\frac{{\sin \,\,A}}{{\sin \,\,B}} = \;\frac{{\sqrt 3 }}{2}\,\,{\rm{and}}\;\,\,\frac{{\cos \,\,A}}{{\cos \,\,B}} = \frac{{\sqrt 5 }}{2},\,\,0 < A,\,\,B < \frac{\pi }{2}\;$, then

$\tan A = \frac{{\sqrt 5 }}{{\sqrt 3 }}$

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

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Application +4 | -1

\;\frac{{\sin \,\,A}}{{\sin \,\,B}} = \;\frac{{\sqrt 3 }}{2}\,\,\mathrm{and}\;\,\,\frac{{\cos \,\,A}}{{\cos \,\,B}} = \frac{{\sqrt 5 }}{2},\,\,0 < A,\,\,B < \frac{\pi }{2}\;

, then

View answer and explanation

Correct option: A

\tan A = \frac{{\sqrt 3 }}{{\sqrt 5 }}

Option A (

\tan A = \frac{{\sqrt 3 }}{{\sqrt 5 }}

) is correct because, by dividing the given equations, we can directly find the value of

\tan A