Let S = - π , π 2 - - π 2 , - π 4 , - 3 π 4 , π 4 . Then the number of elements in the set A = θ ∈ S : tan θ 1 + 5 tan 2 θ = 5 - tan 2 θ is _____ .

Step-by-step solution

Given, S = - π , π 2 - - π 2 , - π 4 , - 3 π 4 , π 4 and the set A = θ ∈ S : tan θ 1 + 5 tan 2 θ = 5 - tan 2 θ Now let tan α = 5 So, tan θ 1 + 5 tan 2 θ = 5 - tan 2 θ becomes, ⇒ tan θ 1 + tan α tan 2 θ = tan α - tan 2 θ On rearranging we get, ⇒ tan θ = tan α - tan 2 θ 1 + tan α tan 2 θ On using formula tan A - B = tan A - tan B 1 - tan A tan B we get, ⇒ tan θ = tan &#9