Trigonometric Equations Question 103
Question: In triangle $ ABC $ if $ \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c} $ , then the triangle is
[Karnataka 1991; Pb. CET 1989]
Options:
A) Right angled
B) Obtuse angled
C) Equilateral
D) Isosceles
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \frac{\cos A}{\cos B}=\frac{a}{b}=\frac{\sin A}{\sin B} $
Þ $ \sin A\cos B=\sin B\cos A $
Þ $ \sin (A-B)=0 $
Þ $ \sin (A-B)=\sin 0 $
Þ $ A-B=0 $
Þ $ A=B $ Similarly, $ A=B=C $ . Hence it is an equilateral triangle.
BETA
