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)

$\frac{1}{\sqrt{2}}$

Answer 2

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