Verify the Identity sin(pi-x)=sin(x)

Problem

sin(π−x)=sin(x)

Solution

1. Identify the appropriate trigonometric identity to use, which is the sine difference formula: sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

2. Substitute the values A=π and B=x into the difference formula.

sin(π−x)=sin(π)*cos(x)−cos(π)*sin(x)

3. Evaluate the trigonometric functions at the specific angle π

sin(π)=0

cos(π)=−1

4. Simplify the expression by plugging these values back into the equation.

sin(π−x)=(0)*cos(x)−(−1)*sin(x)

5. Perform the multiplication and addition to reach the final form.

sin(π−x)=0+sin(x)

sin(π−x)=sin(x)

Final Answer

sin(π−x)=sin(x)

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