Question

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

• A. -7
• B. 6
• C. 4
• D. -5

Answer 1

The correct option is A -7

$\sin \theta =\frac{p}{h}=\frac{24}{25}b=\sqrt{h^2-p^2}=\sqrt{{25}^2-{24}^2}=7$
In second quadrant, both $sec\theta$ and $tan\theta$ are negative.
$\sec \theta =\frac{h}{b}=\frac{-25}{7}\tan \theta =\frac{p}{b}=\frac{-24}{7}\sec \theta +\tan \theta =\frac{-25}{7}+\frac{-24}{7}=-7$