A) \[\frac{a-b}{a-c}\]
B) \[\frac{a+b}{a+c}\]
C) \[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}-{{c}^{2}}}\]
D) \[\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}+{{c}^{2}}}\]
Correct Answer: D
Solution :
\[\frac{1+\cos C\cos (A-B)}{1+\cos (A-C)\cos B}=\frac{1-\cos (A+B)\cos (A-B)}{1-\cos (A-C)\cos (A+C)}\] Þ \[\frac{1-{{\cos }^{2}}A+{{\sin }^{2}}B}{1-{{\cos }^{2}}A+{{\sin }^{2}}C}=\frac{{{\sin }^{2}}A+{{\sin }^{2}}B}{{{\sin }^{2}}A+{{\sin }^{2}}C}=\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}+{{c}^{2}}}\].
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