Question

Show that cos ( 3 17) cos ( 9 17) + 1 2 [cos ( 11 17 ) + cos ( 29 17 ) ] = 0​

Answer 1

Step-by-step explanation:

cos (3π/17) cos (9/17) + (1/2) [cos (11π/ 17) + cos (29π/17)] = 0

LHS = cos (3π/17) сos (9/17) + (1/2) [cos (111/17) + cos (291/17)]

Cos C + Cos D = 2 Cos (C + D)/2 Cos (C -D)/2

C = 29/17, D = 11/17

= cos (3π/17) cos (9/17) + (1/2) [2cos (201/17) cos (9π/17)]

= cos (3π/17) cos (9/17) + cos (π + 3π/ 17) cos (9π/17)

Сos (π + a) = - Cosa

= COS (3π/17) cos (9π/17) + (- сos (3π/ 17) )cos (9π/17)

= cos (3π/17) cos (9/17) - cos (3π/ 17) )cos (9π/17)

= 0

= RHS

QED

Hence proved