Use Identities to find the exact value.24) cos(-75°)

Answer:[tex]\frac{1}{4}[/tex]( [tex]\sqrt{6}[/tex] - [tex]\sqrt{2}[/tex])Step-by-step explanation:Using the addition formula for cosinecos(x - y) = cosxcosy + sinxsinyand the exact valuessin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]cos60° = [tex]\frac{1}{2}[/tex], sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]Note thatcos(- 75)° = cos(45 - 120)°, thuscos(45 - 120)°= cos45° cos120° + sin45° sin120°= cos45° ( - cos60°) + sin45° sin60°= [tex]\frac{1}{\sqrt{2} }[/tex] × - [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex]= - [tex]\frac{1}{2\sqrt{2} }[/tex] + [tex]\frac{\sqrt{3} }{2\sqrt{2} }[/tex]= [tex]\frac{\sqrt{3}-1 }{2\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]= [tex]\frac{\sqrt{2}(\sqrt{3}-1)  }{4}[/tex]= [tex]\frac{1}{4}[/tex]( [tex]\sqrt{6}-\sqrt{2}[/tex])