Simplify cos(pi/3)cos(pi/6)-sin(pi/3)sin(pi/6)

Problem

cos(π/3)*cos(π/6)−sin(π/3)*sin(π/6)

Solution

1. Identify the trigonometric identity for the cosine of a sum of two angles.

cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

2. Substitute the values A=π/3 and B=π/6 into the identity.

cos(π/3+π/6)=cos(π/3)*cos(π/6)−sin(π/3)*sin(π/6)

3. Simplify the sum of the angles inside the cosine function.

π/3+π/6=(2*π)/6+π/6

(2*π)/6+π/6=(3*π)/6

(3*π)/6=π/2

4. Evaluate the cosine of the resulting angle.

cos(π/2)=0

Final Answer

cos(π/3)*cos(π/6)−sin(π/3)*sin(π/6)=0

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