Prove $sin space left parenthesis 2 space sin to the power of negative 1 end exponent space straight x right parenthesis equals space 2 space straight x square root of 1 minus straight x squared end root$

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Solution

Put x = sin θ or θ = sin ^–1x'

therefore space space straight L. straight H. straight S. space space equals space sin left parenthesis 2 space sin to the power of negative 1 end exponent space straight x right parenthesis space equals space sin space left parenthesis 2 space straight theta right parenthesis space space space space space space space space space space space space space space space space equals space 2 space sin space straight theta space cos space straight theta space equals space sin space straight theta space square root of 1 minus sin squared space straight theta end root equals 2 space straight x space square root of 1 minus straight x squared end root equals space straight R. straight H. straight S.

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