KöMaL 2007 C882

The legs of a right-angled triangle are $a$ and $b$. The line segment of length $d$ connecting the vertex of the right angle to a point of the hypotenuse encloses an angle $\delta$ with the leg $a$. Prove that $\frac{1}{d}= \frac{\cos\delta}{a}+ \frac{\sin\delta}{b}.$