The number of values of x ∈ - 2 π , 2 π which satisfy the equation c o s e c x = 1 + cot ⁡ x is equal to

Step-by-step solution

c o s e c x = 1 + cot ⁡ x 1 sin ⁡ x = sin ⁡ x + cos ⁡ x sin ⁡ x ⇒ sin ⁡ x + cos ⁡ x = 1 and sin ⁡ x ≠ 0 ⇒ cos ⁡ x - π 4 = 1 2 ⇒ x - π 4 = ± π 4 , ± 7 π 4 ⇒ x = 0 , π 2 , 2 π , - 3 π 2 But, sin ⁡ x ≠ 0 ⇒ x = π 2 , - 3 π 2