Question

Cos(60*-45*) exact value of expression

Answer 1

Step-by-step explanation:

$\cos(60 \degree - 45 \degree) \\ =\cos \: 60 \degree \: \cos \: 45 \degree + \sin \: 60 \degree \: \sin \: 45 \degree \\ = \frac{1}{2} \times \frac{1}{ \sqrt{2} } + \frac{ \sqrt{3} }{2} \times \frac{1}{ \sqrt{2}} \\ \\ = \frac{1 + \sqrt{3} }{2 \sqrt{2} } \\ \\ =\frac{1 + 1.732}{2 \times 1.414 } \\\\=\frac{2.732}{2.828} \\\\=0.966053748\\\\\approx 0.966\\\\ \red { \boxed{\therefore \: cos(60 \degree - 45 \degree) \approx 0.966 }}$