question_answer

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

A)  \[-\frac{4}{3}\]                  

B) \[-\frac{3}{4}\]

C) \[-\frac{2}{3}\]               

D) \[-\frac{1}{3}\]

Correct Answer: A

Solution :

 Since    \[\sin \theta =\frac{7}{25}\] and \[\theta \] lies in the second quadrant                 \[\therefore \]  \[\sec \theta +\tan \theta =-\frac{25}{24}-\frac{7}{24}\]                 \[=-\frac{32}{24}\]                 \[=-\frac{4}{3}\]