In ∆Abc, Prove the Following: C − B Cos a B − C Cos a = Cos B Cos C - Mathematics

Question

In ∆ABC, prove the following:

\[\frac{c - b \cos A}{b - c \cos A} = \frac{\cos B}{\cos C}\]

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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Sine and Cosine Formulae and Their Applications

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Q 9 Q 8 Q 10

Chapter 10: Sine and cosine formulae and their applications - Exercise 10.2 [Page 25]

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RD Sharma Mathematics [English] Class 11

Chapter 10 Sine and cosine formulae and their applications
Exercise 10.2 | Q 9 | Page 25

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