# How do you evaluate sin(45)cos(15)+cos(45)sin(15)?

Mar 20, 2018

$\therefore \sin 45 \cos 15 + \cos 45 \sin 15 = \sin \left(45 + 15\right) = \sin 60 = \frac{\sqrt{3}}{2}$

#### Explanation:

$\sin 45 \cos 15 + \cos 45 \sin 15$

It is in the form $\sin a \cos b + \cos a \sin b$

But we know $\sin \left(a + b\right) = \sin a \cos b + \cos a \sin b$

$\therefore \sin 45 \cos 15 + \cos 45 \sin 15 = \sin \left(45 + 15\right) = \sin 60 = \frac{\sqrt{3}}{2}$