Simplify sin(pi-x)

Problem

sin(π−x)

Solution

1. Identify the appropriate trigonometric identity for the sine of a difference of two angles.

2. Apply the formula sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B) where A=π and B=x

sin(π−x)=sin(π)*cos(x)−cos(π)*sin(x)

3. Evaluate the known trigonometric values for sin(π) and cos(π)

sin(π)=0

cos(π)=−1

4. Substitute these values back into the expression.

sin(π−x)=(0)*cos(x)−(−1)*sin(x)

5. Simplify the resulting terms.

sin(π−x)=0+sin(x)

sin(π−x)=sin(x)

Final Answer

sin(π−x)=sin(x)

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