If −12≤x≤12, then sin−13x−4x3equals
3sin−1x
π−3sin−1x
−π−3sin−1x
none of these
Let sin−1x=θ. Then, x=sinθ
Also,
−12≤x≤12⇒−12≤sinθ≤12⇒−π6≤θ≤π6.
Now,
sin−13x−4x3=sin−1(sin3θ)⇒ sin−13x−4x3=3θ∵−π6≤0≤π6⇒−π2≤3θ≤π2⇒ sin−13x−4x3=3sin−1x