Question

If $\frac{\sec \theta -\tan \theta }{\sec \theta +\tan \theta }=\frac{36}{49}$, find $\frac{cosec\theta -\sec \theta }{cosec\theta +\sec \theta }$

• A. $\frac{71}{97}$
• B. $\frac{84}{85}$
• C. $\frac{84}{97}$
• D. $\frac{71}{85}$

Answer 1

Answer: (A)

$\frac{71}{97}$

Applying component and dividend, we get
$\frac{2\sec \theta }{2\tan \theta }=\frac{49+36}{49-36}$
$\frac{1}{\sin \theta }=\frac{85}{13}$
Hence
$\sin \theta =\frac{13}{85}$
Hence $\cos \theta =\frac{84}{85}$
Hence
$\text{cosec}\theta =\frac{85}{13}$ and $\sec \theta =\frac{85}{84}$
Substituting in the above equation, we get
$\frac{84-13}{84+13}$
$=\frac{71}{97}$