The number of solutions of the equation | cot x | = cot x + 1 sin x in the interval [ 0 , 2 π ] is

Step-by-step solution

If cot x > 0 ⇒ 1 sin x = 0 (Not possible) If cot x < 0 ⇒ 2 cot x + 1 sin x = 0 ⇒ 2 cos x = - 1 ⇒ x = 2 π 3 or 4 π 3 (reject as cot x < 0 ) So, number of solutions is one.