If \tan \theta=\frac{4}{3}, then the value of \frac{9 \sin \theta+12 \cos \theta}{27 \cos \theta-20 \sin \theta} will be equal to

SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 75 of 100

Marks: +1, -0

\tan θ=\;{4}/{3}

, then the value of

\;{9 \sin θ+12 \cos θ}/{27 \cos θ-20 \sin θ}

will be equal to

Solution:

Given,

\tan θ=\;{4}/{3}

∴ \;{9 \sin θ+12 \cos θ}/{27 \cos θ-20 \sin θ}

=\;{\cos θ ×[{9 \sin θ}/{\cos θ}+12]}/{\cos θ ×[27-20 × \;{\sin θ}/{\cos θ}]}

=\;{9 \tan θ+12}/{27-20 \tan θ}

=\;{9 × {4}/{3}+12}/{27-20 × \;{4}/{3}}=\;{24}/{{1}/{3}}

=24 × 3=72

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