Simplify sin(pi/2+x)

Problem

sin(π/2+x)

Solution

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

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

3. Evaluate the specific trigonometric values for the angle π/2 where sin(π/2)=1 and cos(π/2)=0

4. Simplify the resulting expression by performing the multiplication and addition.

Final Answer

sin(π/2+x)=cos(x)

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