The number of solutions x of the equation sin x + x 2 - sin x 2 = sin x in the interval 2 , 3 is

Step-by-step solution

Given, sin x + x 2 - sin x 2 = sin x ⇒ sin x + x 2 = sin x 2 + sin x ⇒ 2 sin x + x 2 2 cos x + x 2 2 = 2 sin x 2 + x 2 cos x 2 - x 2 sin x + x 2 2 = 0 or cos x 2 + x 2 - cos x 2 - x 2 = 0 x 2 + x 2 = x π or 2 sin x 2 2 sin x 2 = 0 ⇒ x 2 + x 2 = 0 , π , 2 π or x 2 2 = 0 , π , n 2 = 0 , π , 2 π ⇒ x 2 + x = 2 π or x 2 = 2 π ⇒ x 2 + x - 2 π = 0 or x = 2 π ⇒ x = - 1 ± 1 + 8 π 2 or 2 < 2 π < 3 ⇒ 1 + 8 π