Question

If $\sec A=\sqrt{2}$ , find $\frac{3{\cot }^{2}A+2{\sin }^{2}A}{{\tan }^{2}A-{\cos }^{2}A}$.

Answer 1

$\sec A=\sqrt{2}$
$\sec A=\sec 45$
$A={45}^{\circ }$
Now, $\frac{3{\cot }^{2}A+2{\sin }^{2}A}{{\tan }^{2}A-{\cos }^{2}A}$
= $\frac{3{\cot }^{2}45+2{\sin }^{2}45}{{\tan }^{2}45-{\cos }^{2}45}$
= $\frac{3(1{)}^2+2(\frac{1}{\sqrt{2}}{)}^2}{(1{)}^2-(\frac{1}{\sqrt{2}}{)}^2}$
= $\frac{3+1}{\frac{1}{2}}$
= $8$