Question

If ${\cos }^2{45}^o-{\cos }^2{30}^o=x.\cos {45}^o.\sin {45}^o$ then $x=$______.

• A. $-\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $2$
• D. $\frac{3}{4}$

Answer 1

The correct option is A $-\frac{1}{2}$

${\cos }^2{45}^o-{\cos }^2{30}^o=x.\cos {45}^o.\sin {45}^o$
$\therefore {\left(\frac{1}{\sqrt{2}}\right)}^2-{\left(\frac{\sqrt{3}}{2}\right)}^2=x\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{\sqrt{2}}\right)$
$\therefore \frac{1}{2}-\frac{3}{4}=\frac{x}{2}$

$\therefore \frac{2-3}{4}=\frac{x}{2}$

$\therefore -\frac{1}{4}=\frac{x}{2}$

$\therefore x=-\frac{1}{2}$