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the functions inside the Latex script are not being interpreted properly by the Interpreter of the language - today..  there were many other questions - with same difficulty.  So I have changed the answer.  please understand the logic. thanks.

Sin^{-1}x=A, Sin^{-1}(1-x)=B, Cos^{-1}(x)=C\\x=SinA, 1-x=SinB, x=CosC\\CosA=sqrt{(1-x^2)},\\ CosB=sqrt{(1-(1-x)^2)}=sqrt{(2x-x^2)}\\SinC=sqrt{(1-x^2)}\\\\Given,. A+B=C\\...Sin(A+B)=SinC\\SinACosB+SinBCosA=SinC\\

x* sqrt {(2x-x^2)}+(1-x)* sqrt{(1-x^2)}=sqrt{(1-x^2)}\\ x*sqrt{(2x-x^2)}=x*sqrt{(1-x^2)}\\x=0.. is-a-solution\\2x-x^2=1-x^2\\2x=1\\x=1/2\\

So you have two solutions  x =  0 and 1/2.

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some problems with equation editor - LaTex interpreter today. I had to rewrite to be able to display like above.