Question

Evaluate $2cos22\frac{1^{\circ }}{2}\cdot cos67\frac{1^{\circ }}{2}$.

• A. $2$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $0$

Answer 1

Answer: (C)

We have, $2cos22\frac{1^{\circ }}{2}\cdot cos67\frac{1^{\circ }}{2}$
$=cos{\left(22\frac{1}{2}+67\frac{1}{2}\right)}^{\circ }+cos{\left(22\frac{1}{2}-67\frac{1}{2}\right)}^{\circ }$
$=cos90^{\circ }+cos45^{\circ }=0+\frac{1}{\sqrt{2}}$
$=\frac{1}{\sqrt{2}}$