Simplify cos(x+pi/2)

Problem

cos(x+π/2)

Solution

1. Identify the trigonometric identity for the cosine of a sum, 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 known trigonometric values for the angle π/2

cos(π/2)=0

sin(π/2)=1

4. Simplify the expression by plugging these values back into the equation.

cos(x+π/2)=cos(x)*(0)−sin(x)*(1)

cos(x+π/2)=0−sin(x)

Final Answer

cos(x+π/2)=−sin(x)

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