Simplify sin(x+pi/2)

Problem

sin(x+π/2)

Solution

1. Identify the sum formula for sine, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

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

3. Expand the expression using the substitution: sin(x)*cos(π/2)+cos(x)*sin(π/2)

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

5. Simplify the resulting expression: sin(x)*(0)+cos(x)*(1)

Final Answer

sin(x+π/2)=cos(x)

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