Step-by-step explanation:
[tex]\cos(60 \degree - 45 \degree) \\ =\cos \: 60 \degree \: \cos \: 45 \degree + \sin \: 60 \degree \: \sin \: 45 \degree \\ = \frac{1}{2} \times \frac{1}{ \sqrt{2} } + \frac{ \sqrt{3} }{2} \times \frac{1}{ \sqrt{2}} \\ \\ = \frac{1 + \sqrt{3} }{2 \sqrt{2} } \\ \\
=\frac{1 + 1.732}{2 \times 1.414 } \\\\
=\frac{2.732}{2.828} \\\\
=0.966053748\\\\
\approx 0.966\\\\
\red { \boxed{\therefore \: cos(60 \degree - 45 \degree) \approx 0.966 }} \\ [/tex]
