# How do you find the exact value of sin35cos60-cos35sin60 using the sum and difference, double angle or half angle formulas?

May 16, 2017

Answer: $\sin \left(- {25}^{\circ}\right) = \sin \left(335\right)$

#### Explanation:

Consider the difference identity for sine:
$\sin \left(a \pm b\right) = \sin a \cos b \pm \cos a \sin b$

Using this formula, we can see that $a = 35$ and $b = 60$
Therefore:
$\sin 35 \cos 60 - \cos 35 \sin 60$
$= \sin \left(35 - 60\right)$
$= \sin \left(- 25\right)$
$= \sin \left(335\right)$ which is not a special unit circle trig value so we cannot simplify any further