Trigonometric Equations Question 270
Question: In a triangle $ ABC $ , right angled at C, the value of $ \tan A+\tan B $ is
[Pb. CET 1990; Karnataka CET 1999; MP PET 2001]
Options:
A) $ a+b $
B) $ \frac{a^{2}}{bc} $
C) $ \frac{b^{2}}{ac} $
D) $ \frac{c^{2}}{ab} $
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Answer:
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}. $
BETA
