Question

Prove that cos55° + cos65° + cos 175° = 0​

Answer 1

Answer:

0

Step-by-step explanation:

Formula used:

cosC + cosD

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

cos 55° + cos 65° + cos 175°

= cos 55° + (cos 65° + cos 175°)

= cos 55° +

2 cos((65° + 175° )/2) cos((65° -175° )/2)

= cos 55° + 2 cos(120° ) cos(-55°)

= cos 55° + 2 (-1/2 ) cos(-55°)

= cos 55° - cos55°

= 0