Simplify

Problem

sin((7*π)/12)*cos(π/12)−cos((7*π)/12)*sin(π/12)

Solution

1. Identify the trigonometric identity that matches the structure of the expression. The expression follows the form sin(A)*cos(B)−cos(A)*sin(B)

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

3. Substitute the values A=(7*π)/12 and B=π/12 into the identity.

sin((7*π)/12−π/12)

4. Subtract the fractions inside the argument.

(7*π)/12−π/12=(6*π)/12

5. Simplify the resulting fraction.

(6*π)/12=π/2

6. Evaluate the sine of the simplified angle.

sin(π/2)=1

Final Answer

sin((7*π)/12)*cos(π/12)−cos((7*π)/12)*sin(π/12)=1

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