The complete interval of values of x in - π 2 ,   π 2 satisfying the equations cos x · cos   2 x > - 1 4 and 3   cos   x > 1 , is

Step-by-step solution

4   cosx · cos   2 x + 1 > 0 4   cos x 2 cos 2 x - 1 + 1 > 0 8   cos 3 x - 4   cos x + 1 > 0 8 cos 2 x cos x - 1 2 + 4 cos x cos x - 1 2 - 2 cos x - 1 2 > 0 Let cos x = t t - 1 2 8 t 2 + 4 t - 2 > 0 t - 1 2 4 t 2 + 2 t - 1 > 0 t = - 1 ± 5 4 ∴ cos x > 1 3    ∴ 1 ≥ cos x > 1 2 ∴ x ∈ - π 3 , π 3