Find the exact value of the expression.
$\cos80\degree\cos20\degree+\sin80\degree\sin20\degree$

• A. $-\frac12$
• B. 0
• C. $\frac12$
• D. $\frac{\sqrt3}{2}$

Answer: (C)

Verified step by step guidance

1. Recognize that the expression \( \cos 80^\circ \cos 20^\circ + \sin 80^\circ \sin 20^\circ \) resembles the cosine addition formula: \( \cos(a - b) = \cos a \cos b + \sin a \sin b \).
2. Identify the angles in the expression: \( a = 80^\circ \) and \( b = 20^\circ \).
3. Apply the cosine addition formula: \( \cos(80^\circ - 20^\circ) = \cos 80^\circ \cos 20^\circ + \sin 80^\circ \sin 20^\circ \).
4. Calculate the angle difference: \( 80^\circ - 20^\circ = 60^\circ \).
5. Conclude that the expression simplifies to \( \cos 60^\circ \), which is a known trigonometric value.