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2cos^(-1)x=sin^(-1)(2x sqrt(1-x^(2)))" i...

2cos^(-1)x=sin^(-1)(2x sqrt(1-x^(2)))" is valid for "

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cos^(-1)x= 2 sin ^(-1) sqrt((1-x)/(2))=2 cos ^(-1)""sqrt((1+x)/(2))=2tan^(-1)""(sqrt(1-x^(2)))/(1+x)