Prove thatL i) `cos^(-1)(1-2x^(2))=2sin^(-1)x` ii) `cos^(-1)(2x^(2)-1)=2cos^(-1)x`. iii) `sec^(-1)(1

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why sin(2x)=2sin(x)cos(x)

show that (i) sin-1(2x√(1-x^2))=2sin-1 x and (ii) sin-1(2x√(1-x^2))=2cos-1 x

prove that 2cos^-1(x)=cos^-1(2x^2-1)

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To prove that `tan(1/2sin^-1((2x)/(1+x^2))+1/2cos^-1((1-x^2)/(1+x^2))=(2x)/(1-x^2)`

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