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

If x , y , z are in arithmetic progression and tan - 1 ⁡ x , tan - 1 ⁡ y and tan - 1 ⁡ z are also in arithmetic progression, then

Options

  1. Ax = y = z
  2. Bx = y = - z
  3. Cx = 1 , y = 2 , z = 3
  4. Dx = 2 , y = 4 , z = 6

Correct answer

A. x = y = z

Step-by-step solution

Since, x , y , z are in AP ∴ y = x + z 2 ....(i) And tan - 1 ⁡ x , tan - 1 ⁡ y and tan - 1 ⁡ z are also in AP. ∴ 2 tan - 1 ⁡ y = tan - 1 ⁡ x + tan - 1 ⁡ z ⇒ tan - 1 ⁡ 2 y 1 - y 2 = tan - 1 ⁡ x + z 1 - x z ⇒ 2 y 1 - y 2 = 2 y 1 - x z [from equation. (i)] ⇒ y 2 = x z ⇒ x , y , z are in GP. ∴ x = y = z

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