Use a sum or difference formula to find the exact value of t

Use a sum or difference formula to find the exact value of the following. cos 17/30 cos 11/60 - sin 17/30 sin 11/60

Solution

cos 17/30 cos 11/60 - sin 17/30 sin 11/60

use the formula : cos(A +B) = cosAcosB - sinAsinB

cos 17/30 cos 11/60 - sin 17/30 sin 11/60

A = 17pi ; B = 11pi/60

So,  cos 17/30 cos 11/60 - sin 17/30 sin 11/60

=cos(17pi/30 +11pi/60)

=cos((34pi +11pi)/60)

= cos45pi/60

=cos15pi/20

=cos(3pi/4)

= - 1/sqrt2