To solve the equation sin(2x+π/2) = sin(x+π/4), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b).

Applying this identity to the equation, we have:

sin(2x)cos(π/2) + cos(2x)sin(π/2) = sin(x)cos(π/4) + cos(x)sin(π/4)

Since cos(π/2) = 0 and sin(π/2) = 1, the equation simplifies to:

sin(2x) = sin(x)cos(π/4) + cos(x)sin(π/4)

Using the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b) again, we can rewrite the equation as:

sin(2x) = sin(x + π/4)

Now, we can use the double angle identity sin(2x) = 2sin(x)cos(x) to further simplify the equation:

2sin(x)cos(x) = sin(x + π/4)

Next, we can use the sum-to-product identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b) to rewrite sin(x + π/4) as:

sin(x)cos(π/4) + cos(x)sin(π/4)

Substituting this back into the equation, we have:

2sin(x)cos(x) = sin(x)cos(π/4) + cos(x)sin(π/4)

Now, we can simplify the equation by factoring out sin(x) and cos(x):

sin(x)(2cos(x) - cos(π/4)) = cos(x)(sin(π/4) - 2)

Since sin(π/4) = cos(π/4) = 1/√2, the equation becomes:

sin(x)(2cos(x) - 1/√2) = cos(x)(1/√2 - 2)

Now, we can divide both sides of the equation by cos(x) to eliminate the cos(x) term:

sin(x)(2 - 1/√2) = 1/√2 - 2

Simplifying further, we have:

sin(x)(2√2 - 1) = 1/√2 - 2

Finally, we can divide both sides of the equation by (2√2 - 1) to solve for sin(x):

sin(x) = (1/√2 - 2)/(2√2 - 1)

This is the solution for sin(2x+π/2) = sin(x+π/4).