# How do you use the product to sum formulas to write 10cos75^circcos15^circ as a sum or difference?

Jun 12, 2017

= 5/2

#### Explanation:

Use trig identity:
$\cos a . \cos b = \left(\frac{1}{2}\right) \left(\cos \left(a + b\right) + \cos \left(a - b\right)\right)$.
In this case:
$10 \cos 75. \cos 15 = \left(\frac{10}{2}\right) \left(\cos 90 + \cos 60\right)$
Since cos 90 = 0, and $\cos 60 = \frac{1}{2}$, therefore

10cos 75.cos 15 = 5/2