Respuesta :
Answer:
[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
Step-by-step explanation:
Using the difference formula for cosine and the exact values
cos45° = sin45° = [tex]\frac{\sqrt{2} }{2}[/tex], cos30° = [tex]\frac{\sqrt{3} }{2}[/tex], sin30° = [tex]\frac{1}{2}[/tex]
cos(a - b) = cosacosb + sinasinb
Note 15° = 45° - 30°, thus
cos15°
= 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]
Answer:
[tex]\frac{\sqrt{6} +\sqrt{2} }{4}[/tex]
Step-by-step explanation:
