JEE Main202529 Jan 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Let ( S = x: ⁻¹ x= + ⁻¹ x+ ⁻¹(2 x+1) ). Then ( _ x ~S (2 x-1)^2 ) is equal to ______.

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Step-by-step solution

aligned & ⁻¹ x= + ⁻¹ x+ ⁻¹(2 x+1) & 2 ⁻¹ x- ⁻¹(2 x+1)= 3 2 & 2 - = 3 2 where ⁻¹ x= , ⁻¹(2 x+1)= & 2 = 3 2 + & 2 = & 2 ^2 -1= & 2 x^2-1=2 x+1 & x^2-x-1=0 aligned aligned & n = 1 5 2 = [ array c n = 1+ 5 2 rejected n = 1- 5 2 array . & 4 x ^2-4 x =4 & (2 x -1)^2=5 aligned

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