Question

If $\cos 2A=\frac{7}{19}$, calculate the value of $\frac{1}{{\cos }^{2}A-{\sin }^{2}A}$.

• A. $0.18$
• B. $0.37$
• C. $0.74$
• D. $1.36$
• E. $2.71$

Answer 1

The correct option is E $2.71$

Given, $\cos 2A=\frac{7}{19}$

$\Rightarrow \cos 2A=2{\cos }^{2}A-1=\frac{7}{19}$
$\Rightarrow 2{\cos }^{2}A=\frac{26}{19}$

$\Rightarrow {\cos }^{2}A=\frac{13}{19}$
$\Rightarrow {\sin }^{2}A=1-{\cos }^{2}A=1-\frac{13}{19}=\frac{6}{19}$
Therefore value of $\frac{1}{{\cos }^{2}A-{\sin }^{2}A}=\frac{1}{\frac{13}{19}-\frac{6}{19}}=\frac{1}{\frac{7}{19}}=\frac{19}{7}=2.71$