Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
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

  1. Ax 1+x^2
  2. Bx
  3. C1+x^2
  4. 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

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All MHT CET PYQs