TS EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), if \(\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\), then \(\triangle A B C\) is
- A right angled
- B isosceles right angled
- C equilateral
- D scalene
Answer & Solution
Correct Answer
(C) equilateral
Step-by-step Solution
Detailed explanation
\(\text { In } \triangle A B C, \frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\) By sine rule, \(\begin{array}{lc} \Rightarrow & \frac{\cos A}{k \sin A}=\frac{\cos B}{k \sin B}=\frac{\cos C}{k \sin C} \\ \Rightarrow & \cot A=\cot B=\cot C \\ \Rightarrow & A=B=C \end{array}\)…
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