Question

prove that 2cosπ/13×cos9π/13+cos3π/13+cos5π/13=0

Answer 1

cosa + cosb = 2cos(a+b)/2cos(a-b)/2
2cosπ/13 × cos9π/13 + 2cos4π/13cos(-π/13)
cos(-a) = cosa
taking 2cosπ/13 common , we get :
2cosπ/13(cos9π/13 + cos4π/13)
2cosπ/13 × 2 cosπ/2 × cos0
cosπ/2 = 0
therefore , 2cosπ/13×cos9π/13+cos3π/13 + cos5π/13 = 0

Answer 2

Answer:

Step-by-step explanation:

cosa + cosb = 2cos(a+b)/2cos(a-b)/2

2cosπ/13 × cos9π/13 + 2cos4π/13cos(-π/13)

cos(-a) = cosa

taking 2cosπ/13 common , we get :

2cosπ/13(cos9π/13 + cos4π/13)

2cosπ/13 × 2 cosπ/2 × cos0

cosπ/2 = 0

therefore , 2cosπ/13×cos9π/13+cos3π/13 + cos5π/13 = 0