Question

Cos3x - cos5x + cos7x=0 Find general solution?​

Answer 1

Answer:

Cosx + Cos3x + Cos5x + Cos7x = 0

⇒Cosx + Cos7x + Cos3x + Cos5x = 0

⇒2Cos4x.Cos3x + 2Cos4x.Cosx = 0

⇒Cos4x (Cos3x + Cosx) = 0

⇒Cos4x (2Cos2x.Cosx) = 0

⇒Cosx.Cos2x.Cos4x = 0

⇒Cosx = 0 or Cos2x = 0 or Cos4x = 0

⇒x = nπ/8 [Where n can be any integer except multiple of 8]