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InterviewSolution
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If \(\rm \frac{{\sin \left( {x\; + \;y} \right)}}{{\sin \left( {x\; - \;y} \right)}} = \frac 53\) then what is \(\rm \frac{{\tan x}}{{\tan y}}\) equal to?1. 22. 43. \(\frac 1 4\)4. \(\frac 12\) |
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Answer» Correct Answer - Option 2 : 4 Concepts: If \(\rm \frac A B = \frac C D\), property of componendo and dividendo is given by, \(\rm \frac{A+B}{A-B}=\frac{C+D}{C-D}\) Formula:
Calculation: Given: \(\rm \frac{{\sin \left( {x\; + \;y} \right)}}{{\sin \left( {x\; - \;y} \right)}} = \frac 53\) \(\Rightarrow\rm \;\frac{{\sin x\cos y\; + \;\cos x\sin y}}{{\sin x\cos y\; - \;\cos x\sin y}} = \frac 53\) Using componendo and dividendo formula, we get \(\rm \Rightarrow \frac{{(\sin x\cos y + \cos x\sin y) + (\sin x\cos y - \cos x\sin y)}}{{(\sin x\cos y + \cos x\sin y) - (\sin x\cos y - \cos x\sin y)}} = \frac{5+3}{5-3}\) \(\rm \Rightarrow \;\frac{{2{\rm{\;sin}}x\cos y}}{{2\cos x\sin y}} = \frac{8}{2}\) \(\rm \therefore \frac{{\tan x}}{{\tan y}} = 4\) |
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