Triangles And Properties Of Triangle Question 14
Question: In triangle ABC given $ 9a^{2}+9b^{2}-17c^{2}=0. $ If $ \frac{cotA+cotB}{\cot C}=\frac{m}{n}, $ then the value of $ (m+n) $ equals
Options:
A) 13
B) 5
C) 7
D) 9
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{\cot A+\cot B}{\cot C}=\frac{\sin (A+B)}{sinAsinB}.\frac{\sin C}{\cos C} $ $ =\frac{{{\sin }^{2}}C}{\sin A\sin B\cos C}=\frac{c^{2}}{ab}.\frac{2ab}{a^{2}+b^{2}-c^{2}} $ $ =\frac{2c^{2}}{a^{2}+b^{2}-c^{2}}=\frac{2c^{2}}{\frac{17c^{2}}{9}-c^{2}}=\frac{9}{4}=\frac{m}{n} $
$ \Rightarrow (m+n)=9+4=13 $
BETA
