MHT CET20243 May 2024Evening ShiftMathematicsInverse Trigonometric FunctionsActual
If 0 x 1 ; then 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 2 =
Options
- Ax 1+x^2
- Bx
- C1+x^2
- Dx 1+x^2
Correct answer
D. x 1+x^2
Step-by-step solution
Given, 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 2 Let ⁻¹ x= aligned & x= & = 1 1+x^2 ...(i) & = x 1+x^2 ...(ii) aligned aligned & 1+x^2 [ x ( ⁻¹ x )+ ( ⁻¹ x ) ^2-1 ]^ 1 2 & = 1+x^2 [ x + ^2-1 ]^ 1 2 & = 1+x^2 [ x x 1+x^2 + 1 1+x^2 ^2-1 ]^ 1 2 & = 1+x^2 [ ( x^2+1 1+x^2 )^2-1 ]^ 1 2 = & 1+x^2 [ ( 1+x^2 )^2-1 ]^ 1 2 = & 1+x^2 (1+x^2-1 )^ 1 2 = & x 1+x^2 aligned