Verified answer

Note that cos(A) - cos(B) = -2*sin[(A+B)/2]*sin[(A-B)/2].

Then,

cos(π/11) - cos(π/2)

= -2*sin[{(π/11) + (π/2)}/2]*sin[{(π/11) - (π/2)}/2]

= -2*sin(13π/44)*sin(-9π/44)

= 2*sin(13π/44)*sin(9π/44)