Question

The exact value of the expression.

$\cos 80°\cos 20°+\sin 80°\sin 20°$

Short answer

The value of$\cos 80°\cos 20°+\sin 80°\sin 20°$is$\frac{1}{2}$

Step-by-step solution

Step 1. Given information 

The given expression is$\cos 80°\cos 20°+\sin 80°\sin 20°$

Step 2. Find the value of cos80°cos20°+sin80°sin20° 

We know that,

$\cos \left(\alpha -\beta \right)=\cos \alpha \cos \beta +\sin \alpha \cos \beta$

$$\begin{gathered} \cos 80°\cos 20°+\sin 80°\sin 20°=\cos \left(80°-20°\right) \\ =\cos 60° \\ =\frac{1}{2}\left[\sin 60°=\frac{1}{2}\right] \end{gathered}$$