Simplify

Problem

cos((5*π)/12)*cos(π/12)+sin((5*π)/12)*sin(π/12)

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=(5*π)/12 and B=π/12 to match the given expression.

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

cos((5*π)/12−π/12)

4. Subtract the fractions inside the argument.

(5*π)/12−π/12=(4*π)/12

5. Simplify the fraction by dividing the numerator and denominator by 4.

(4*π)/12=π/3

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

cos(π/3)=1/2

Final Answer

cos((5*π)/12)*cos(π/12)+sin((5*π)/12)*sin(π/12)=1/2

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