UPSC NDA Math Model Paper 8

Given: 8 tan(2x) – 5 = 3
⇒ 8 tan(2x) = 8
⇒ tan 2x = 1
As we know that, tan (π/4) = 1
⇒ tan 2x = tan (π/4)
As we know that, if tan θ = tan α then θ = nπ + α, α ∈ (-π/2, π/2), n ∈ Z.
⇒ 2x = nπ + (π/4), where n ∈ Z.
⇒ x = n (π/2) + (π/8), where n ∈ Z.