Simplify sin(pi/2-x)

Problem

sin(π/2−x)

Solution

1. Identify the trigonometric identity for the sine of a difference of two angles, which is sin(A−B)=sin(A)*cos(B)−cos(A)*sin(B)

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

3. Apply the formula to get sin(π/2)*cos(x)−cos(π/2)*sin(x)

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

5. Simplify the expression to (1)*cos(x)−(0)*sin(x) which results in cos(x)

Final Answer

sin(π/2−x)=cos(x)

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