Find the Exact Value cos(60-45)

Problem

cos(60−45)

Solution

1. Identify the appropriate trigonometric identity for the cosine of a difference, which is cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

2. Substitute the values A=60 and B=45 into the identity.

cos(60−45)=cos(60)*cos(45)+sin(60)*sin(45)

3. Evaluate the exact values of the trigonometric functions for the given angles.

cos(60)=1/2

cos(45)=√(,2)/2

sin(60)=√(,3)/2

sin(45)=√(,2)/2

4. Multiply the terms together.

1/2⋅√(,2)/2=√(,2)/4

√(,3)/2⋅√(,2)/2=√(,6)/4

5. Combine the fractions to find the final exact value.

√(,2)/4+√(,6)/4=(√(,2)+√(,6))/4

Final Answer

cos(60−45)=(√(,2)+√(,6))/4

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