Simplify

Problem

cos(π/12)*cos(−π/6)+sin(π/12)*sin(−π/6)

Solution

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

2. Assign the values A=π/12 and B=−π/6 to match the given expression to the identity.

3. Apply the identity to rewrite the expression as a single cosine function.

cos(π/12−(−π/6))

4. Simplify the argument of the cosine by finding a common denominator for the fractions.

π/12+π/6=π/12+(2*π)/12=(3*π)/12

5. Reduce the fraction inside the cosine function.

(3*π)/12=π/4

6. Evaluate the cosine of the resulting angle using the unit circle or standard trigonometric values.

cos(π/4)=√(,2)/2

Final Answer

cos(π/12)*cos(−π/6)+sin(π/12)*sin(−π/6)=√(,2)/2

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