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Inverse Trigonometric Functions

JEE Main 2024 (Online) 4th April Evening ShiftMCQMedium📈 Topic in 21% papers+4−1
Ques. 1JEE Main 2024, 4 April (Evening Shift)

Given that the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [-1, 1] such that -1x - -1y = , - 2 . Then, the minimum value of x2 + y2 + 2xy is

  1. 0
  2. -1
  3. 12
  4. -12

Answer

(1) 0

Solution

-1y = 2 - -1y ⇒ -1x + -1y = 2 +

Take cos: xy - 1 - x2 1 - y2 = ( 2 + ) = -

xy + = 1 - x2 1 - y2

Square: x2y2 + 2xy + 2 = 1 - x2 - y2 + x2y2

x2 + y2 + 2xy = 2 0

Minimum = 0 (at = 2, e.g. x = y = 0)

Answer: (1)

Keep practising — Inverse Trigonometric Functions

Ques. 2JEE Main 2024, 31 January (Morning Shift)

For , , 0, if -1 + -1 + -1 = and ( + + )( - + )=3 , then equals

  1. 3
  2. 32
  3. 1 2
  4. 3-12 2
Ques. 3JEE Main 2024, 31 January (Evening Shift)

If a= -1( (5)) and b= -1( (5)), then a2+b2 is equal to

  1. 25
  2. 4 2+25
  3. 8 2-40 +50
  4. 4 2-20 +50
Ques. 4JEE Main 2024, 29 January (Evening Shift)

Let x= mn (m, n are co-prime natural numbers) be a solution of the equation (2 -1x )= 19 and let , ( > ) be the roots of the equation mx2-nx-m+n=0. Then the point ( , ) lies on the line

  1. 3x-2y=-2
  2. 3x+2y=2
  3. 5x+8y=9
  4. 5x-8y=-9
Ques. 5JEE Main 2024, 27 January (Evening Shift)

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying -1(x)+ -1(2x)= 4 is :

  1. more than 2
  2. 2
  3. 0
  4. 1

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