Question

2cos4 theta + 1/2cos theta+1 = (2cos theta- 1) (2 cos 2 theta- 1)​

Answer 1

Given trigonometric equation :

2 Sin² Ф - 2 Cos Ф = 1/2

2 ( 1- cos²Ф) - 2 cosФ  = 1/2

2 Cos² Ф + 2 Cos Ф - 3/2 = 0

4 Cos² Ф + 4 Cos Ф - 3 = 0

Cos Ф =  [-2 + √(4+12) ] /4

           =  1/2  or  -3/2

Since  CosФ is always between -1 and 1,  :  Cos Ф = 1/2

   

 Ф = 60°

Answer 2

Answer:

Given trigonometric equation :

2 Sin² Ф - 2 Cos Ф = 1/2

2 ( 1- cos²Ф) - 2 cosФ = 1/2

2 Cos² Ф + 2 Cos Ф - 3/2 = 0

4 Cos² Ф + 4 Cos Ф - 3 = 0

Cos Ф = [-2 + √(4+12) ] /4

= 1/2 or -3/2

Since CosФ is always between -1 and 1, : Cos Ф = 1/2

Ф = 60°