A) 1
B) 2
C) 3
D) 0
Correct Answer: B
Solution :
| [b] We have, \[\cos ec\,\,\,A=\sqrt{2}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\angle A=45{}^\circ \] \[[\cos ec\,\,45{}^\circ =\sqrt{2}]\] |
| \[\therefore \,\,\,\frac{2{{\sin }^{2}}A+3{{\cot }^{2}}A}{4({{\tan }^{2}}A-{{\cos }^{2}}A)}=\frac{2{{\sin }^{2}}45{}^\circ +3{{\cot }^{2}}45{}^\circ }{4({{\tan }^{2}}45{}^\circ -{{\cos }^{2}}45{}^\circ )}\] |
| \[=\frac{2\times {{\left( \frac{1}{\sqrt{2}} \right)}^{2}}+3\times {{1}^{2}}}{4\left( {{1}^{2}}-{{\left( \frac{1}{\sqrt{2}} \right)}^{2}} \right)}=\frac{1+3}{4\times \frac{1}{2}}=\frac{4}{2}=2\] |
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