Simplify cos(60+x)

Problem

cos(60^∘+x)

Solution

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

2. Substitute the values A=60^∘ and B=x into the identity.

cos(60^∘+x)=cos(60^∘)*cos(x)−sin(60^∘)*sin(x)

3. Evaluate the exact trigonometric values for the known angle 60^∘

cos(60^∘)=1/2

sin(60^∘)=√(,3)/2

4. Substitute these values back into the expression.

cos(60^∘+x)=1/2*cos(x)−√(,3)/2*sin(x)

5. Factor out the common denominator to simplify the final expression.

cos(60^∘+x)=(cos(x)−√(,3)*sin(x))/2

Final Answer

cos(60^∘+x)=(cos(x)−√(,3)*sin(x))/2

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