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TS EAMCET · Maths · Properties of Triangles

In any \(\triangle A B C, \frac{b-c \cos A}{c-b \cos A}\) is equal to

  1. A \(\frac{\sin B}{\sin C}\)
  2. B \(\frac{\cos C}{\cos B}\)
  3. C \(\frac{\cos B}{\cos C}\)
  4. D \(\frac{\sin C}{\sin B}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\cos C}{\cos B}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} \frac{b-c \cos A}{c-b \cos A} & =\frac{b-\frac{b^2+c^2-a^2}{2 b}}{c-\frac{b^2+c^2-a^2}{2 c}} \\ & =\left(\frac{b^2+a^2-c^2}{c^2+a^2-b^2}\right) \times \frac{c}{b} \\ & =\frac{b^2+a^2-c^2}{2 a b} \cdot \frac{2 a c}{c^2+a^2-b^2} \\ & =\frac{\cos C}{\cos…