A) \[1\]
B) \[-1\]
C) \[2\]
D) \[0\]
Correct Answer: A
Solution :
| [a] We have, \[\frac{x\cos e{{c}^{2}}30{}^\circ \,\,{{\sec }^{2}}45{}^\circ }{8{{\cos }^{2}}45{}^\circ {{\sin }^{2}}60{}^\circ }={{\tan }^{2}}60{}^\circ -{{\tan }^{2}}30{}^\circ \] |
| \[\Rightarrow \,\,\,\,\,\,\frac{x{{(2)}^{2}}\,{{(\sqrt{2})}^{2}}}{8{{\left( \frac{1}{\sqrt{2}} \right)}^{2}}{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}}={{(\sqrt{3})}^{2}}-{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,\frac{8x}{3}=3-\frac{1}{3}\Rightarrow \frac{8x}{3}=\frac{8}{3}\Rightarrow x=\frac{3}{8}\times \frac{8}{3}=1\] |
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