A) \[|a|\,\,\le 4\]
B) \[|a|\,\,\le 2\]
C) \[|a|\,\,\le \sqrt{3}\]
D) \[|a|\,\,\le \sqrt{2}\]
Correct Answer: C
Solution :
\[{{\tan }^{4}}x-2{{\sec }^{2}}x+{{a}^{2}}=0\] \[\Rightarrow \] \[{{\tan }^{4}}x-2(1+{{\tan }^{2}}x)+{{a}^{2}}=0\] \[\Rightarrow \] \[{{\tan }^{4}}x-2{{\tan }^{2}}x+1=3-{{a}^{2}}\] \[\Rightarrow \] \[{{({{\tan }^{2}}x-1)}^{2}}=3-{{a}^{2}}\] \[\Rightarrow \] \[3-{{a}^{2}}\ge 0\] \[\Rightarrow \] \[{{a}^{2}}\le 3\] \[\Rightarrow \] \[|a|\,\,\le \sqrt{3}\]
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