Expand Using Sum/Difference Formulas cos(-15)

Problem

cos(−15)

Solution

1. Identify a pair of common angles from the unit circle whose sum or difference equals −15 We can use 30 and 45

−15=30−45

2. Apply the formula for the cosine of a difference, which is cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

cos(30−45)=cos(30)*cos(45)+sin(30)*sin(45)

3. Substitute the known trigonometric values for the angles.

cos(30)=√(,3)/2

cos(45)=√(,2)/2

sin(30)=1/2

sin(45)=√(,2)/2

4. Multiply the terms together.

√(,3)/2⋅√(,2)/2=√(,6)/4

1/2⋅√(,2)/2=√(,2)/4

5. Combine the fractions over a common denominator.

√(,6)/4+√(,2)/4=(√(,6)+√(,2))/4

Final Answer

cos(−15)=(√(,6)+√(,2))/4

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