Simplify cos(x-pi)

Problem

cos(x−π)

Solution

1. Identify the appropriate trigonometric identity for the cosine of a difference, which is cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

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

cos(x−π)=cos(x)*cos(π)+sin(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.

cos(x−π)=cos(x)*(−1)+sin(x)*(0)

cos(x−π)=−cos(x)

Final Answer

cos(x−π)=−cos(x)

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