Verify the Identity cos(x-pi/2)=sin(x)

Problem

cos(x−π/2)=sin(x)

Solution

1. Identify the appropriate trigonometric identity to use for the left side of the equation, which is the cosine difference formula.

2. Apply the formula cos(α−β)=cos(α)*cos(β)+sin(α)*sin(β) where α=x and β=π/2

3. Substitute the values into the formula:

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

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

5. Simplify the expression by multiplying the terms:

cos(x)*(0)+sin(x)*(1)=sin(x)

Final Answer

cos(x−π/2)=sin(x)

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