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

Problem

cos(x+π/2)=−sin(x)

Solution

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

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

3. Expand the expression using 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 substituting these values:

cos(x+π/2)=cos(x)*(0)−sin(x)*(1)

6. Finalize the simplification to reach the right-hand side of the identity:

cos(x+π/2)=−sin(x)

Final Answer

cos(x+π/2)=−sin(x)

Want more problems? Check here!