Question

If $\sin \theta =\frac{7}{25}$ and ${90}^0<\theta <{180}^0$, then find the value of $\sec \theta +\tan \theta$.

Answer 1

Since $\theta$ lies in the second quadrant $\sec \theta$ and $\tan \theta$ are both negative
i.e. $\sec \theta =-\frac{25}{24}$
and $\tan \theta =-\frac{7}{24}$
$\therefore \sec \theta +\tan \theta =-\frac{25}{24}-\frac{7}{24}=\frac{32}{24}$
$=-\frac{4}{3}$