It is known that \( \sin \beta=\frac{4}{5} \) and \( 0\beta\pi \) then the value of \[ \frac{\sq...

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It is known that \( \sin \beta=\frac{4}{5} \) and \( 0\beta\pi \) then the value of
\[
\frac{\sqrt{3} \sin (\alpha+\beta)-\frac{2}{\cos \pi / 6} \cos (\alpha+\beta)}{\sin \alpha}
\]
is
(a) Independent of \( \alpha \) for all \( \beta \) in \( (0, \pi) \)
(b) \( \frac{5}{13} \) for \( \tan \beta0 \)
(c) \( \frac{3(7+24 \cot \alpha)}{15} \) for \( \tan \beta0 \)
(d) None of these
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