Question

If $\sin \theta =\frac{24}{25}$ and $\theta$ lies in the second quadrant, then $\sec \theta +\tan \theta =$

• A. $7$
• B. $-7$
• C. $\frac{1}{7}$
• D. $\frac{-1}{7}$

Answer 1

The correct option is B

$-7$

Since $\theta$ lies in the second quadrant, $\theta$ varies from $\frac{\pi }{2}$ to $\pi$.

Applying Pythagoras's theorem in $△$AOP

${25}^2$ = ${24}^2$ + ${OA}^2$

$OA=7$ on the negavtive x - axis.

Since, $P$ lies in second quadrant, $\sec \theta$ and $\tan \theta$ will be negative and $OA=7$

So,
The value of $\sec \theta +\tan \theta$
$=-\frac{25}{7}-\frac{24}{7}$
$=\frac{-49}{7}$
$=-7$