Simplify sin(pi/2-u)

Problem

sin(π/2−u)

Solution

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

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

3. Substitute the known values for the trigonometric functions at π/2 specifically sin(π/2)=1 and cos(π/2)=0

4. Simplify the resulting expression by performing the multiplication.

1⋅cos(u)−0⋅sin(u)

5. Finalize the result by removing the zero term.

cos(u)

Final Answer

sin(π/2−u)=cos(u)

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