Let α and β be non zero real numbers such that 2 cos ⁡ β - cos ⁡ α + cos…

Let α and β be non zero real numbers such that 2cos⁡β-cos⁡α+cos⁡αcos⁡β=1. Then which of the following is/are true?
  1. tan⁡α2-3tan⁡β2=0
  2. 3tan⁡α2-tan⁡β2=0
  3. tan⁡α2+3tan⁡β2=0
  4. 3tan⁡α2+tan⁡β2=0

Solution

2cos⁡β-cos⁡α+cos⁡αcos⁡β-1=0        .....(i)

Use   cos⁡β=1-tan2⁡β21+tan2⁡β2 and cos⁡α=1-tan2⁡α21+tan2⁡α2 in (i)

We get tan2⁡α2=3tan2⁡β2 ⇒ tan⁡α2+3tan⁡β2=0 or tan⁡α2- 3tan⁡β2=0

Asked in: JEE Advanced 2017 (Paper 2)

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