Simplify cos(pi-x)

Problem

cos(π−x)

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=π and B=x into the identity.

3. Evaluate the known trigonometric values for the angle π where cos(π)=−1 and sin(π)=0

4. Simplify the resulting expression by performing the multiplication and addition.

Final Answer

cos(π−x)=−cos(x)

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