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Question
In ∆ABC, prove the following:
\[\frac{c - b \cos A}{b - c \cos A} = \frac{\cos B}{\cos C}\]
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Solution
\[LHS = \frac{c - b\cos A}{b - c\cos A}\]
=`{a cos B+b cos A-b cos A}/{a cos C+c cos A-c cos A}` `["Using projection formula"]`
`c= a cos B+b cos A, b= a cos C+c cos A]`
\[ = \frac{a\cos B}{a\cos C}\]
\[ = \frac{\cos B}{\cos C} = RHS\]
Hence proved.
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