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

Problem

sin(x−π/2)=−cos(x)

Solution

1. Identify the difference 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.

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

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

sin(x−π/2)=sin(x)*(0)−cos(x)*(1)

4. Simplify the expression by performing the multiplication.

sin(x−π/2)=0−cos(x)

sin(x−π/2)=−cos(x)

Final Answer

sin(x−π/2)=−cos(x)

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