In any ΔABC, prove that C - b cosA/b - c cosA = cosB/cosC

Question

In any ΔABC, prove that

\(\frac{c-bcosA}{b-ccosA}\) = \(\frac{cosB}{cosC}\)

Answer 1

Need to prove: \(\frac{c-bcosA}{b-ccosA}\) = \(\frac{cosB}{cosC}\)

Left hand side

= \(\frac{c-bcosA}{b-ccosA}\)

[Multiplying the numerator and denominator by 1/a]

= \(\frac{cosB}{cosC}\)

= Right hand side. [proved]