Question

Evaluate $2\,cos\,22 \frac{1^{\circ}}{2}\cdot cos\,67 \frac{1^{\circ}}{2}$.

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

Answer 1

Answer: (C)

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