Answers

2015-07-11T19:16:22+05:30
A is acute and cosec A = √2
⇒ A = 45°

 \frac{2\ sin^2A+3\ cot^2A}{tan^2A-cos^2A}\\ \\ =  \frac{2\ sin^245^0+3\ cot^245^0}{tan^245^0-cos^245^0}\\ \\ = \frac{2 \times (1/ \sqrt{2})^2 +3 \times (1)^2}{(1)^2-(1/ \sqrt{2})^2 }\\ \\ = \frac{2 \times (1/2)+3}{1-(1/2)}\\\\= \frac{1+3}{1/2}\\\\= \frac{4}{1/2}\\\\=\boxed{8}
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