The number of solutions of the equation tan ⁡ x + sec ⁡ x = 2 cos ⁡ x lying in the interval 0,5 π is

Step-by-step solution

tan ⁡ x + sec ⁡ x = 2 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 2 , - 1 sin ⁡ x = - 1 ⇒ cos ⁡ x = 0 and hence tan ⁡ x ,   sec ⁡ x is not defined So, sin ⁡ x = 1 2 Hence, in 0,5 π there are 6 solutions.