A) \[{{45}^{o}}\]or \[{{135}^{o}}\]
B) \[{{135}^{o}}\]or \[{{120}^{o}}\]
C) \[{{30}^{o}}\]or \[{{60}^{o}}\]
D) None of these
Correct Answer: A
Solution :
\[2{{a}^{2}}{{b}^{2}}+2{{b}^{2}}{{c}^{2}}={{a}^{4}}+{{b}^{4}}+{{c}^{4}}\] Also,\[{{({{a}^{2}}-{{b}^{2}}+{{c}^{2}})}^{2}}=\] \[{{a}^{4}}+{{b}^{4}}+{{c}^{4}}-2({{a}^{2}}{{b}^{2}}+{{b}^{2}}{{c}^{2}}-{{c}^{2}}{{a}^{2}})\] Þ \[{{({{a}^{2}}-{{b}^{2}}+{{c}^{2}})}^{2}}=2{{c}^{2}}{{a}^{2}}\]Þ\[\frac{{{a}^{2}}-{{b}^{2}}+{{c}^{2}}}{2ca}=\pm \frac{1}{\sqrt{2}}=\cos B\] Þ \[B={{45}^{o}}\]or \[{{135}^{o}}\].
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