MCQ
If \[\frac{160}{3}\] \[\tan \theta = \frac{a}{b}, \text{ then } \frac{a \sin \theta + b \cos \theta}{a \sin \theta - b \cos \theta}\]
Options
\[\frac{a^2 + b^2}{a^2 - b^2}\]
\[\frac{a^2 - b^2}{a^2 + b^2}\]
\[\frac{a + b}{a - b}\]
\[\frac{a - b}{a + b}\]
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Solution
Given :` tan θ = a/b'
We have to find the value of following expression in terms of a and b
We know that: `tanθ="Perpendicular"/"Base"`
⇒`" Base" =b`
⇒` "Perpendicular=a"`
⇒`" Hypotenuse"=sqrt (a^2+b^2)`
Now we find,
`(a sinθ+b cos θ)/(a sinθ-b cos θ)=(a(a/(a^2+b^2))+b (b/(a^2+b^2)))/(a(a/(a^2+b^2))-b(b/(a^2+b^2)))`
=`((a^2+b^2)/(a^2+b^2))/((a^2-b^2)/(a^2+b^2))`
=`(a^2+b^2)/(a^2-b^2)`
Hence the correct option is (a)
Is there an error in this question or solution?
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