Verify the Identity sin(pi/2-x)=cos(x)

Problem

sin(π/2−x)=cos(x)

Solution

1. Identify the appropriate trigonometric identity to use, which is the sine difference formula: sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

2. Substitute the values A=π/2 and B=x into the difference formula.

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

3. Evaluate the trigonometric constants using the unit circle, where sin(π/2)=1 and cos(π/2)=0

sin(π/2−x)=(1)*cos(x)−(0)*sin(x)

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

sin(π/2−x)=cos(x)−0

sin(π/2−x)=cos(x)

Final Answer

sin(π/2−x)=cos(x)

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