Simplify (sin(pi/2-x))/(cos(pi/2-x))

Problem

sin(π/2−x)/cos(π/2−x)

Solution

1. Apply co-function identities to the numerator and the denominator.

2. Substitute sin(π/2−x)=cos(x) into the numerator.

3. Substitute cos(π/2−x)=sin(x) into the denominator.

4. Simplify the resulting fraction using the definition of the cotangent function.

cos(x)/sin(x)=cot(x)

Final Answer

sin(π/2−x)/cos(π/2−x)=cot(x)

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