The number of roots of the equation tan ⁡ x + sec ⁡ x =2 cos ⁡ x in 0 , 4 π is

Step-by-step solution

tan ⁡ x + sec ⁡ x = 2 cos ⁡ x Multiplying by cos ⁡ x , sin ⁡ x + 1 = 2 cos 2 ⁡ x = 2 - 2 sin 2 ⁡ x ⇒ 2 sin 2 ⁡ x + sin ⁡ x - 1 = 0 ⇒ sin ⁡ x = - 1 , 1 2 sin ⁡ x = 1 2 at x = π 6 , 5 π 6 in 0,2 π sin ⁡ x = 1 2 → four times in 0,4 π sin ⁡ x = - 1 ⇒ x = 3 π 2 for which t a n x and s e c x are not defined ⇒ sin ⁡ x = - 1 is not possible ⇒ Number of roots in 0,4 π is 4 .