Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If x satisfies the inequality t a n - 1 x 2 + 3 t a n - 1 x - 4 > 0 , then the complete set of values of x is

Options

  1. A- tan ⁡ 4 , π 4
  2. B- ∞ , tan ⁡ 4 ∪ π 4 , ∞
  3. Ctan ⁡ 1 , ∞
  4. Dtan ⁡ 4 , tan ⁡ 1

Correct answer

C. tan ⁡ 1 , ∞

Step-by-step solution

Let, t a n - 1 x = t the given inequality becomes t 2 + 3 t - 4 > 0 ⇒ t + 4 t - 1 > 0 ∴ t < - 4 or t > 1 t a n - 1 x < - 4 (not possible) or t a n - 1 x > 1 ⇒ x > tan ⁡ 1

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

Considering only the principal values of the inverse trigonometric functions, the value of ⁻¹( (-11)) + 10 (2 ⁻¹ ( 1 2 ) ) + 10 (2 ⁻¹(2)) is 2026Let = 3 ⁻¹ ( 6 11 ) and = 3 ⁻¹ ( 4 9 ) , where inverse trigonometric functions take only the principal values. Given below are two statements: Statement I: ( + ) > 0 . Statement II 2026If ( ⁻¹(x 2 )) = ( ⁻¹ 1-x^2 ) , x (0,1) , then the value of x is : 2026Let [ ] denote the greatest integer function. If the domain of the function f(x) = ⁻¹ ( x+[x] 3 ) is [ , ) , then ^2 + ^2 is equal to: 2026Let 0 < < 1 , = 1 3 and ⁻¹(1- ) + ⁻¹(1- ) = 4 . Then 6( + ) is equal to: 2026If 4 + _ p=1 ¹¹ ⁻¹ ( 2^ p-1 1 + 2^ 2p-1 ) = , then is equal to __________. 2026If y = ⁻¹ ( 3 x - 4 x 4 x + 3 x ) + 2 ⁻¹ ( x 1+ 1-x^2 ) , then dy dx at x = 3 2 is equal to: 2026Considering the principal values of inverse trigonometric functions, the value of the expression (2 ⁻¹ ( 2 13 )-2 ⁻¹ ( 3 10 ) ) is equal to : 2026 Full Inverse Trigonometric Functions list All NTA Abhyas JEE Main PYQs