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Question

Prove the following,

3sin1x=sin1(3x4x3),xϵ[12,12]

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Solution

Let sin1x=θx=sinθ, then
LHS = 3sin1x=3sin1(sinθ)=3θ
RHS = sin1(3x4x3)=sin1[3sinθ4sin3θ]=sin1[sin3θ]=3θ
[( sin3θ=3sinθ4sin3θ]
LHS=RHS Hence proved.


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