Find the Exact Value cos((13pi)/15)cos(-pi/5)-sin((13pi)/15)sin(-pi/5)

$\cos (\frac{13 π}{15}) \cos (- \frac{π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{13 π}{15}) \cos (\frac{9 π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$

Step 2

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{13 π}{15}) \cos (\frac{9 π}{5}) - \sin (\frac{13 π}{15}) \sin (\frac{9 π}{5})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{13 π}{15}) \cos (\frac{9 π}{5}) - \sin (\frac{13 π}{15}) \sin (\frac{9 π}{5})$

Decimal Form:

$- 0.5$