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Inverse Trigonometric Functions

JEE Main 2026 (Online) 28th January Morning ShiftNumericalMedium📈 Topic in 10% papers+4
Ques. 1JEE Main 2026, 28 January (Morning Shift)

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

Answer

1

Solution

Let -1 23 = 2 : 2 = 1 - 231 + 23 = 15 = 1 5

( 4 + ) = 1 + 1 51 - 1 5 = 5 + 1 5 - 1 = 3 + 52

Let -1 23 = 2 , so 2 = 53 and

= 2 1 + 2 = 231 + 53 = 23 + 5 = 3 - 52

Hence k = 3 + 52 + 3 - 52 = 3, and the equation is

-1(3x - 1) = -1x - -1x = 2 -1x - 2

For the domain, -1 3x - 1 1 and -1 x 1, so 0 x 23.

Taking sine: 3x - 1 = (2 -1x - 2 ) = - (2 -1x) = -(1 - 2x2)

2x2 - 3x = 0 x = 0 or x = 32, which is rejected as it lies outside the domain.

Check x = 0: LHS = -1(-1) = - 2, RHS = 0 - 2 = - 2 ✓

number of solutions = 1

Answer: 1

Keep practising — Inverse Trigonometric Functions

Ques. 2JEE Main 2026, 28 January (Evening Shift)

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

  1. 3356
  2. - 3356
  3. - 1663
  4. 1663
Ques. 3JEE Main 2026, 24 January (Evening Shift)

If the domain of the function f(x) = -1 ( 1x2 - 2x - 2 ) is (- , ] [ , ] [ , ), then + + + is equal to

  1. 4
  2. 2
  3. 5
  4. 3
Ques. 4JEE Main 2026, 22 January (Morning Shift)

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

  1. 2
  2. 0
  3. 3
  4. 1
Ques. 5JEE Main 2026, 21 January (Morning Shift)

If the domain of the function f(x) = -1 ( 2x - 511 - 3x ) + -1(2x2 - 3x + 1) is the interval [ , ], then + 2 is equal to :

  1. 5
  2. 2
  3. 3
  4. 1
Ques. 6JEE Main 2026, 21 January (Evening Shift)

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 .

Ques. 7JEE Main 2025, 8 April (Evening Shift)

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

  1. - 32
  2. + 52
  3. - 54
  4. + 32
Ques. 8JEE Main 2025, 4 April (Morning Shift)

Considering the principal values of the inverse trigonometric functions, -1 ( 32x + 12 1 - x2 ), - 12 < x < 1 2, is equal to

  1. -5 6 - -1x
  2. 5 6 - -1x
  3. 6 + -1x
  4. 4 + -1x
Ques. 9JEE Main 2025, 4 April (Evening Shift)

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

  1. 2+ -1 ( 12 )
  2. 2- -1 ( 12 )
  3. 2- -1 ( 12 )
  4. 2+ -1 ( 12 )
Ques. 10JEE Main 2025, 2 April (Evening Shift)

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .

Ques. 11JEE Main 2025, 29 January (Morning Shift)

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

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