Simplify cos(x-pi/2)

Problem

cos(x−π/2)

Solution

1. Identify the cosine difference identity, which is cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

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

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

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

cos(x−π/2)=cos(x)*(0)+sin(x)*(1)

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

cos(x−π/2)=0+sin(x)

cos(x−π/2)=sin(x)

Final Answer

cos(x−π/2)=sin(x)

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