Question

If sin $\theta =\frac{7}{25}and\theta$ lies in the second quadrant, then the value of sec $\theta +tan\theta$

• A. $-\frac{4}{3}$
• B. $-\frac{3}{4}$
• C. $-\frac{2}{3}$
• D. $-\frac{1}{3}$

Answer 1

The correct option is A $-\frac{4}{3}$

$sin\theta =\frac{perpendicular}{hypotenuse}=\frac{7}{25}$
$perpendicular=7$
$hypotenuse=25$
Therefore
$base=\sqrt{hypotenuse{}^2-perpendicular{}^2}$
$=\sqrt{25{}^2-49}$
hence $base=24$
$sec\theta +tan\theta$
$=-\frac{25}{24}-\frac{7}{24}$ ...($tan\theta$ and $sec\theta$ is negative as $\theta$ is in second quadrant)
$=\frac{-25-7}{24}$
$=\frac{-32}{24}$
$=-\frac{4}{3}$
Hence answer is A