Question

${\cos }^2{60}^{\circ }+{\sin }^2{30}^{\circ }=\frac{1}{a}$
Then $a=$

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

Answer 1

The correct option is A $2$

${\cos }^2{60}^{\circ }+{\sin }^2{30}^{\circ }$
$={\left(\frac{1}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2$
$=\frac{1}{4}+\frac{1}{4}$
$=\frac{2}{4}$
$=\frac{1}{2}$

$\therefore \frac{1}{a}=\frac{1}{2}$

$\Rightarrow a=2$