Answer:
see explanation
Step-by-step explanation:
Using the addition formula for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
and exact values
sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]
c0s30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]
Express cos15° = cos(45 - 30 )°, then
cos(45 - 30)°
= cos45°cos30° + sin45°sin30°
= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )
= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]
= [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex] ← exact value
