Answer
Use a scientific calculator to evaluate the given expression and obtain:
$\cos{\left(\frac{7\pi}{9}\right)}\cos{\left(\frac{2\pi}{9}\right)}-\sin{\left(\frac{7\pi}{9}\right)}\sin{\left(\frac{2\pi}{9}\right)}=-1$
Work Step by Step
Use a scientific calculator to evaluate the given expression to obtain:
$\cos{\left(\frac{7\pi}{9}\right)}\cos{\left(\frac{2\pi}{9}\right)}-\sin{\left(\frac{7\pi}{9}\right)}\sin{\left(\frac{2\pi}{9}\right)}=-1$