Question

(if sec theta + tan theta)/(sec theta - tan theta)=5/3 then sin theta is says to?

Answer 1

$\textbf{Given:}$

$\displaystyle\frac{sec\,\theta+tan\,\theta}{sec\,\theta-tan\,\theta}=\frac{5}{3}$

$\textbf{To find: }sin\theta$

$\displaystyle\frac{sec\,\theta+tan\,\theta}{sec\,\theta-tan\,\theta}=\frac{5}{3}$

$\displaystyle\,3(sec\,\theta+tan\,\theta)=5(sec\,\theta-tan\,\theta)$

$\displaystyle\,3sec\,\theta+3tan\,\theta=5sec\,\theta-5tan\,\theta$

$\displaystyle\,3sec\,\theta-5sec\,\theta=-3tan\,\theta-5tan\,\theta$

$\displaystyle\,-2sec\,\theta=-8tan\,\theta$

$\displaystyle\,sec\,\theta=4tan\,\theta$

$\displaystyle\,\frac{1}{cos\,\theta}=4\frac{sin\,\theta}{cos\,\theta}$

$\displaystyle\,4\,sin\,\theta=1$

$\implies\bf\displaystyle\,sin\,\theta=\frac{1}{4}$

$\therefore\textbf{The value of \bf\,sin\,\theta is \bf\frac{1}{4} }$

$\implies\textbf{Option (A) is correct}$

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