Question

If $\sin \theta =\frac{7}{25}$ then $\sec \theta +\tan \theta$ is

• A. $\frac{19}{25}$
• B. $\frac{16}{25}$
• C. $\frac{4}{3}$
• D. $\frac{24}{25}$

Answer 1

The correct option is C $\frac{4}{3}$

Since, $sin\theta =\frac{7}{25}$

$\Rightarrow \cos \theta =\sqrt{1-{\sin }^2\theta }=\sqrt{1-\frac{49}{625}}=\sqrt{\frac{576}{625}}=\frac{24}{25}$
Now,

$\sec \theta +\tan \theta =\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }$
$=\frac{1+\sin \theta }{\cos \theta }$$=\frac{1+\frac{7}{25}}{\frac{24}{25}}$ $=\frac{32}{24}$$=\frac{4}{3}$

Option C is correct.