Answer:
[tex]\frac{1}{4}[/tex] ( [tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex] )
Step-by-step explanation:
Using the trigonometric identity
cos(a + b) = cosacosb - sinasinb
Note [tex]\frac{5\pi }{12}[/tex] = [tex]\frac{\pi }{4}[/tex] + [tex]\frac{\pi }{6}[/tex], thus
cos ([tex]\frac{5\pi }{12}[/tex] )
= cos( [tex]\frac{\pi }{4}[/tex] + [tex]\frac{\pi }{6}[/tex] )
= cos ([tex]\frac{\pi }{4}[/tex] ) cos[tex]\frac{\pi }{6}[/tex] ) - sin (
= ([tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) - (
= [tex]\frac{\sqrt{6} }{4}[/tex] - [tex]\frac{\sqrt{2} }{4}[/tex]
= [tex]\frac{1}{4}[/tex] ([tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex] )
