Question

Solve the equation for all radian solutions in [0.27). Start by replacing cos 2x with its Double Angle formula cos 2x - 3cos x + 2 = 0

Answer 1

cos 2x - 3Cosa +2=0 2nt I 1 i NE ZL. The given eanation Cosax - 3 Cosa +2=0 ar 2005 2.6051 -1 -36032 +2=0 (using Double angle cos 26 = 2.039- Blosk+1=0 OV 2 losun - cosa cosat 1-0 2003*(C3*) -(652-1) = 0 (2 (es -1)( Cosx-1) = 0 ex Cether acosx-1=0 or Cosx-1=0 Now 2 Cosa-1=0 تا Cos o = cosery O= 2n1t& inea For neo, For n=1 2 - x= 1/3 € [ 0,20) - 17/3 4 [0, 20) 21 + 173 $ 60,20) 3x = 21T - 173 = 5473 € [°91) 1973 ¢ 10,2n) Therefore the solution of the eavertin 2 Cosx-120 in the internal [ 0, 21) are 7/2, 59/ For n=2, 2 474 -

Aganin cosx-1=0 cos a = 1 -coso ant to in EZ an то, For & [0,201) x= oe [0,20) n=1, x=20 n2-1, x=-28 [°211) Therefore the salleen of the equation Cosx-1=0 in the interned 20, 21) is Hence the solution of the internet [0, 21) are o, 1/3, 57/3. given eauartion in the Hence Aus! o, 1/3, 52