Expand Using Sum/Difference Formulas cos(45-60)

Problem

cos(45−60)

Solution

1. Identify the appropriate trigonometric identity for the cosine of a difference.

cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

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

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

3. Evaluate the trigonometric functions for the given angles using the unit circle.

cos(45)=√(,2)/2

cos(60)=1/2

sin(45)=√(,2)/2

sin(60)=√(,3)/2

4. Multiply the terms together.

cos(45−60)=√(,2)/2⋅1/2+√(,2)/2⋅√(,3)/2

cos(45−60)=√(,2)/4+√(,6)/4

5. Combine the fractions over a common denominator.

cos(45−60)=(√(,2)+√(,6))/4

Final Answer

cos(45−60)=(√(,2)+√(,6))/4

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