Trigonometry

If 5(tan2 x – cos2x) = 2 cos 2x + 9, then the value of cos 4x is

  1. -3/5
  2. 1/3
  3. 2/9
  4. -7/9

Solution

5(sec2 x – 1 – cos2 x) = 2(2cos2 x – 1) + 9

Let cos2 x = t

5(1/t - 1 - t) = 2(2t - 1) + 9

5(1 – t – t2) = 4t2 + 7t

9t2 + 12t – 5 = 0

t = 1/3, -5/3

cos2 x = 1/3

cos 2x = 2/3 - 1 = -1/3

cos 4x = -7/9

The correct option is D.