Prove the following,
3sin−1x=sin−1(3x−4x3),xϵ[−12,12]
Let sin−1x=θ⇒x=sinθ, then LHS = 3sin−1x=3sin−1(sinθ)=3θ RHS = sin−1(3x−4x3)=sin−1[3sinθ−4sin3θ]=sin−1[sin3θ]=3θ [(∵ sin3θ=3sinθ−4sin3θ] ∴ LHS=RHS Hence proved.
Prove: 3sin−1x=sin−1(3x−4x3),x∈[−12,12]
Prove that :3sin−1x=sin−1(3x−4x3),xϵ[−12,12].