Simplify sin(x-pi)

Problem

sin(x−π)

Solution

1. Identify the angle subtraction identity for the sine function, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

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

sin(x−π)=sin(x)*cos(π)−cos(x)*sin(π)

3. Evaluate the trigonometric constants cos(π) and sin(π)

cos(π)=−1

sin(π)=0

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

sin(x−π)=sin(x)*(−1)−cos(x)*(0)

sin(x−π)=−sin(x)

Final Answer

sin(x−π)=−sin(x)

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