Let tan - 1 x ∈ - π 2 , π 2 , for x ∈ ℝ . Then the number of real solutions of the equation 1 + cos 2 x = 2 tan - 1 tan x in the set - 3 π 2 , - π 2 ∪ - π 2 , π 2 ∪ π 2 , 3 π 2 is equal to

Step-by-step solution

Given, 1 + cos 2 x = 2 tan - 1 tan x ⇒ 2 cos 2 x = 2 tan - 1 tan x ⇒ cos x = tan - 1 tan x Now plotting the diagram of cos x   &   tan - 1 tan x we get, Now from above diagram we can say that, Number of solutions = Number of intersection points = 3