Question

Choose the correct answer from the alternatives given.
If $\frac{sec\theta +tan\theta }{sec\theta -tan\theta }=\frac{51}{79}$, then the value of $sin\theta$ is

• A. 65/144
• B. 39/72
• C. 91/144
• D. 35/72

Answer 1

The correct option is A 65/144

$\displaystyle\, \frac{Sec \theta + Tan \theta}{Sec \theta Tan \theta} = 2 - \frac{51}{79}$
$\displaystyle\, \frac{Sec \theta + Tan \theta}{Sec \theta Tan \theta} = \frac{209}{79}$
Applying Componendo and Dividendo,
$\frac{Sec\theta +Tan\theta +Sec\theta Tan\theta }{Sec\theta Tan\theta [sec\theta +Tan\theta ]}=\frac{209+79}{20979}$
$\displaystyle\, \frac{2 sec \theta}{2 Tan \theta} = \frac{288}{130}$
$\displaystyle\, \frac{sec \theta }{Tan \theta} = \frac{288}{130}$
$\frac{1}{Sin\theta }=\frac{288}{130}\Rightarrow Sin\theta =\frac{65}{144}$