Simplify cos(270-x)

Problem

cos(270−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=270 and B=x into the identity.

cos(270−x)=cos(270)*cos(x)+sin(270)*sin(x)

3. Evaluate the trigonometric functions at the quadrantal angle 270 where cos(270)=0 and sin(270)=−1

cos(270−x)=(0)*cos(x)+(−1)*sin(x)

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

cos(270−x)=−sin(x)

Final Answer

cos(270−x)=−sin(x)

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