8.025. $\sin \left(15^{\circ}+x\right)+\sin \left(45^{\circ}-x\right)=1$.

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8.025. $\sin \left(15^{\circ}+x\right)+\sin \left(45^{\circ}-x\right)=1$.
## Solution.

We have:

$$
2 \sin \frac{15^{\circ}+x+45^{\circ}-x}{2} \cos \frac{15^{\circ}+x-45^{\circ}+x}{2}=1, \quad \cos \left(x-15^{\circ}\right)=1
$$

Then $x-15^{\circ}=360^{\circ} k, x=15^{\circ}+360^{\circ} k, k \in Z$.

Answer: $\quad x=15^{\circ}+360^{\circ} k, \quad k \in Z$.