Inverse Trigonometric Functions: JEE Questions & Solutions

If the domain of the function f(x) = ^-1 ( 2x-511-3x) + ^-1(2x^2-3x+1) is the interval [, ], then + 2 is equal to:

Let the maximum value of ( ^-1x)^2 + ( ^-1x)^2 for x [ - 32, 1 2 ] be mn ^2, where (m, n) = 1. Then m + n is equal to.

The number of solutions of ^-1(4x) + ^-1(6x) = 6, where - 12 6 < x < 12 6, is equal to

If the domain of the function f(x)= ^-1 ( 1x^2-2x-2) is (-,) [, ] [,), then + + + is equal to

If k= ( 4+ 12 ^-1 ( 23)) + ( 12 ^-1 ( 23)), then the number of solutions of the equation ^-1(kx-1)= ^-1x- ^-1x is:

Considering the principal values of inverse trigonometric functions, the value of (2 ^-1 2 13-2 ^-1 3 10) is equal to:

Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of 16(( ^-1x)^2+( ^-1x)^2)…

If 2 x 3 4, then ^-1 ( 1213 x + 513 x) is equal to:

If 0, then the expression ^-1 + ( 1 + ^2 -) + ^-1 + ( 1 + ^2 -) + ^-1 + ( 1 + ^2 -) is equal to:

The value of ( ^-1 (- 35) + ^-1 ( 513) + ^-1 (- 3365)) is:

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

If y = ( 3 + ^-1 x2), then (x - y)^2 + 3y^2 is equal to.

Considering the principal values of the inverse trigonometric functions, ^-1 ( 32 x + 12 1-x^2), - 12 < x < 1 2, is equal to

The value of ^-1 ( 1 + ^2(2) - 1 (2)) - ^-1 ( 1 + ^2 ( 12) + 1 ( 12)) is equal to:

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying (x) + (2x) = 4…

Let x = mn (m, n are co-prime natural numbers) be a solution of the equation (2 ^-1 x) = 19, and let, () be the roots of the equation mx^2…

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 ^-1(x) + 3 ^-1(x) = 2 5 is:

If the sum of all the solutions of ^-1 ( 2x1-x^2) + ^-1 ( 1-x^22x) = 3, where -1 < x < 1, x 0, is - 4 3, then is equal to.

Let a1 = 1, a2, a3, a4, be consecutive natural numbers. Then ^-1 ( 11 + a1 a2) + ^-1 ( 11 + a2 a3) + + ^-1 ( 11 + a2021a2022) is equal to:

If ^-1 ( 17) + ^-1 ( 45) - ^-1 ( 7736) = 0, 0 < < 13, then ^-1 () + ^-1 () is equal to:

Let (a, b) (0, 2) be the largest interval for which ^-1() - ^-1() 0, (0, 2) holds. If x^2 + x + ^-1 ( (x^2 - 6x + 10)) + ^-1 ( (x^2 - 3)^2…

Let S be the set of all solutions of the equation ^-1(2x) - 2 ^-1( 1 - x^2) =, x [ - 12, 12 ]. Then x S 2 ^-1(x^2 - 1) is equal to:

Let S = x R: 0 < x < 1 and 2 ^-1 ( 1-x1+x) = ^-1 ( 1-x^21+x^2). If n(S) denotes the number of elements in S, then:

The range of f(x) = 4 ^-1 ( x^2x^2 + 1) is: