Simplify cos(pi/2-x)

Problem

cos(π/2−x)

Solution

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

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

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

3. Evaluate the known trigonometric values for the angle π/2

cos(π/2)=0

sin(π/2)=1

4. Substitute these values back into the expression.

cos(π/2−x)=(0)*cos(x)+(1)*sin(x)

5. Simplify the resulting expression.

cos(π/2−x)=sin(x)

Final Answer

cos(π/2−x)=sin(x)

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