A) \[\frac{1}{4}\]
B) 4
C) 2
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
Given, \[4x=\cos ec\theta \] and \[\frac{4}{x}=\cot \,\theta \] \[x=\frac{\cos ec\theta }{4}\] and \[\frac{1}{x}=\frac{\cot \theta }{4}\] We have find the value of \[4\left[ {{x}^{2}}-\frac{1}{{{x}^{2}}} \right]\] \[=4\left[ {{\left( \frac{\cos ec\theta }{4} \right)}^{2}}-{{\left( \frac{\cot \theta }{4} \right)}^{2}} \right]\] \[=4\left[ \frac{\cos e{{c}^{2}}\theta }{16}-\frac{{{\cot }^{2}}\theta }{16} \right]\] \[=\frac{4}{16}\left[ \cos e{{c}^{2}}\theta -{{\cot }^{2}}\theta \right]=\frac{1}{4}\]
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