Expand the Trigonometric Expression cos(pi/2-x)

Problem

cos(π/2−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/2 and B=x into the identity.

cos(π/2−x)=cos(π/2)*cos(x)+sin(π/2)*sin(x)

3. Evaluate the known trigonometric constants cos(π/2)=0 and sin(π/2)=1

cos(π/2−x)=(0)*cos(x)+(1)*sin(x)

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

cos(π/2−x)=0+sin(x)

cos(π/2−x)=sin(x)

Final Answer

cos(π/2−x)=sin(x)

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