Question

The value of ${\left(\frac{\sin {47}^o}{\cos {43}^o}\right)}^2+{\left(\frac{\cos {43}^o}{\sin {47}^o}\right)}^2-4{\cos }^2{45}^o$ is :

• A. $2$
• B. $0$
• C. $1$
• D. $3$

Answer 1

The correct option is B $0$

The value of ${\left(\frac{\sin {47}^o}{\cos {43}^o}\right)}^2+{\left(\frac{\cos {43}^o}{\sin {47}^o}\right)}^2-4{\cos }^2{45}^o$ is
$={\left[\frac{\sin {47}^o}{{\cos (90-47)}^o}\right]}^2+{\left[\frac{\cos {43}^o}{{\sin (90-43)}^o}\right]}^2-{4\left(\frac{1}{\sqrt{2}}\right)}^2$
$={\left(\frac{\sin 47}{\sin 47}\right)}^2+{\left(\frac{\cos 43}{\cos 43}\right)}^2-4\left(\frac{1}{2}\right)$

$={\left(1\right)}^2+{\left(1\right)}^2-4\times \frac{1}{2}$

$=1+1-2=0$