The number of roots of the equation, 81 sin 2 x + 81 cos 2 x = 30 in the interval 0 , π is equal to :

Step-by-step solution

81 sin 2 x + 81 cos 2 x = 30 81 sin 2 x + 81 1 81 sin 2 x = 30 81 sin 2 x = t t + 81 t = 30 t 2 - 30 t + 81 = 0 t - 3 t - 27 = 0 81 sin 2 x = 3 1 or 81 sin 2 x = 3 3 3 4 sin 2 x = 3 1 or 3 4 sin 2 x = 3 3 sin 2 x = 1 4 or sin 2 x = 3 4 Hence, total 4 solution.