Let α and β be non zero real numbers such that 2 cos ⁡ β - cos ⁡ α + cos ⁡ α cos ⁡ β = 1 . Then which of the following is/are true?

Step-by-step solution

2 cos ⁡ β - cos ⁡ α + cos ⁡ α cos ⁡ β - 1 = 0 .....(i) Use cos ⁡ β = 1 - tan 2 ⁡ β 2 1 + tan 2 ⁡ β 2 a n d cos ⁡ α = 1 - tan 2 ⁡ α 2 1 + tan 2 ⁡ α 2 in (i) We get tan 2 ⁡ α 2 = 3 tan 2 ⁡ β 2 ⇒ tan ⁡ α 2 + 3 tan ⁡ β 2 = 0 o r tan ⁡ α 2 - 3 tan ⁡ β 2 = 0