Find the value of x: $\sin(x) = \cos(x)$ for x in [0, $\pi/2$].

Step 1: Rewrite the equation

The given equation is $\sin(x) = \cos(x)$. To solve for $x$, we can divide both sides by $\cos(x)$, provided that $\cos(x) \neq 0$. This will allow us to express the equation in terms of $\tan(x)$.

Step 2: Divide by $\cos(x)$

Dividing both sides of the equation by $\cos(x)$ gives us $\frac{\sin(x)}{\cos(x)} = 1$. We know that $\frac{\sin(x)}{\cos(x)}$ is equal to $\tan(x)$.

Step 3: Express in terms of $\tan(x)$

Substituting $\tan(x)$ for $\frac{\sin(x)}{\cos(x)}$, the equation simplifies to $\tan(x) = 1$. Now we need to find the value of $x$ for which the tangent is 1.

Step 4: Find the value of $x$

We are looking for the angle $x$ in the interval $[0, \pi/2]$ whose tangent is 1. We know that $\tan(\pi/4) = 1$. Therefore, $x = \pi/4$. This value lies within the given interval.

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