Question

If $\sqrt{2}\cos A=1$ then the value of ${\tan }^{4}A+{\cot }^{4}A$

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. 2
• D. 1

Answer 1

The correct option is C 2

Since, $\sqrt{2}\cos A=1$
$\Rightarrow \cos A=\frac{1}{\sqrt{2}}$
Since, $\cos \theta =\frac{\text{base}}{\text{hypotenuse}}$
Here, base = 1 and hypotenuse = $\sqrt{2}$
using pythagoras
$H^2=P^2+B^2$
$(\sqrt{2}{)}^2=P^2+1^2$
$P=1$
$\therefore \tan A=\frac{\text{perpendicular}}{\text{base}}=1$
and
$\cot A=\frac{\text{base}}{\text{perpendicular}}=1$
$\therefore {\tan }^{4}A+{\cot }^{4}A=1^4+1^4=2$
Option C is correct.