UPSC NDA Math Model Paper 7

Given: 4 sin 3x = 2
⇒ sin 3x =1/2
As we know that, sin (π/6) = 1/2
⇒ sin 3x = sin (π/6)
As we know that, if sin θ = sin α then θ = nπ + (- 1)‌n α, α ∈ [-π/2, π/2], n ∈ Z.
⇒ 3x = nπ + (- 1)‌n × (π/6), where n ∈ Z.
⇒ x = n × (π/3) + (- 1)‌n × (π/18), where n ∈ Z.