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

Problem

sin(π/2+x)=cos(x)

Solution

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

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

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

4. Simplify the expression by multiplying the terms.

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

sin(π/2+x)=(1)*cos(x)+(0)*sin(x)

sin(π/2+x)=cos(x)

Final Answer

sin(π/2+x)=cos(x)

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