A) \[a+b\]
B) \[\frac{{{a}^{2}}}{bc}\]
C) \[\frac{{{b}^{2}}}{ac}\]
D) \[\frac{{{c}^{2}}}{ab}\]
Correct Answer: D
Solution :
Given, A right-angled triangle ABC with right angled at C. Let a, b and c be the lengths of sides BC, CA and AB respectively. We know from the Pythagoras theorem that \[{{c}^{2}}={{a}^{2}}+{{b}^{2}}\]and\[\tan A=\frac{a}{b}.\] Similarly, \[\tan B=\frac{b}{a}.\] Therefore, \[\tan A+\tan B=\frac{a}{b}+\frac{b}{a}=\frac{{{a}^{2}}+{{b}^{2}}}{ab}=\frac{{{c}^{2}}}{ab}.\]You need to login to perform this action.
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