Simplify cos(pi+x)

Problem

cos(π+x)

Solution

1. Identify the appropriate trigonometric identity for the cosine of a sum of two angles.

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

cos(π+x)=cos(π)*cos(x)−sin(π)*sin(x)

3. Evaluate the known trigonometric values for the angle π

cos(π)=−1

sin(π)=0

4. Substitute these values back into the expression.

cos(π+x)=(−1)*cos(x)−(0)*sin(x)

5. Simplify the resulting expression by performing the multiplication.

cos(π+x)=−cos(x)

Final Answer

cos(π+x)=−cos(x)

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