question_answer

If in  \[\Delta \,ABC,\]\[\angle \] A = \[90{}^\circ \]. BC = a, AC = b and AB = c. then the value of tan B + tan C is

A)  \[\frac{{{c}^{2}}}{ab}\]                    

B)  \[\frac{{{a}^{2}}+{{c}^{2}}}{b}\]

C)  \[\frac{{{b}^{2}}}{ac}\]                    

D)  \[\frac{{{a}^{2}}}{bc}\]

Correct Answer: D

Solution :

  \[\tan \,B\,=\frac{AC}{AB}=\frac{b}{c}\] \[\tan \,C\,=\frac{AB}{AC}=\frac{c}{b}\] \[\therefore \] \[\tan \,B\,+\tan \,C=\frac{b}{c}+\frac{c}{b}\] \[=\frac{{{b}^{2}}+{{c}^{2}}}{bc}=\frac{{{a}^{2}}}{bc}\]