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

Problem

cos(π/2+x)=−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 the values A=π/2 and B=x into the sum formula.

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

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

cos(π/2+x)=(0)*cos(x)−(1)*sin(x)

4. Simplify the expression by performing the multiplication.

cos(π/2+x)=0−sin(x)

5. Conclude that the left side equals the right side.

cos(π/2+x)=−sin(x)

Final Answer

cos(π/2+x)=−sin(x)

Want more problems? Check here!