Question

Show that cos42°+cos78°+cos162°=0.​

Answer 1

Answer:

cos42° + cos78° + cos162°

= cos(160° - 18°) + cos(60 + 18°) + cos(18 - 18)

= cos60° cos18° + sin60° sin18° + cos60° cos11° - sin60 sin18 - cos18°

= 2cos60° cos18° - cot18°

= 2 × 1/2 cos18° - cos18°

= 2 × 1/2 cos18° - cos18°

= 2 × 1/2 cos18° - cos18°

= cos18° - cos18° - cos18°

= 0

L.H.S = R.H.S

Hence, verified.