Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If ∑ k = 1 n tan - 1 1 k 2 + k + 1 = tan - 1 θ , then θ =

Options

  1. An n + 2
  2. Bn n + 1
  3. C1
  4. Dn n - 1

Correct answer

A. n n + 2

Step-by-step solution

It is given that, ∑ k = 1 n tan - 1 1 k 2 + k + 1 = tan - 1 θ Simplifying the above expression we get, ∑ k = 1 n tan - 1 ( k + 1 ) - k 1 + k ( k + 1 ) = tan - 1 θ ⇒ ∑ k = 1 n tan - 1 ( k + 1 ) - tan - 1 k = tan - 1 θ tan - 1 2 - tan - 1 1 + tan - 1 3 - tan - 1 2 + tan - 1 4 - tan - 1 3 + … + tan - 1 ( n + 1 ) - tan - 1 n = tan - 1 θ ⇒ tan - 1 ( n + 1 ) - tan - 1 1 = tan - 1 θ ⇒ tan - 1 n + 1 - 1 1 + n + 1 = tan - 1 θ ⇒ n 2 + n = θ

Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

If y = ⁻¹ ( 1+x^3 + 1-x^3 1+x^3 - 1-x^3 ) then dy dx = 2026If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is: 2026The value of the expression ⁻¹ ( 7 6 ) + ⁻¹ ( 22 3 ) + ⁻¹ ( 4 5 ) is: 2026Which of the following is the simplest form of the expression ⁻¹ ( 1+x^2 - 1 x ) where x 0 2026If ⁻¹ x + ⁻¹ y = 2 , then x^2 is equal to 2026⁻¹ ( 1 1 + 1 2 ) + ⁻¹ ( 1 1 + 2 3 ) + + ⁻¹ ( 1 1 + n(n+1) ) = 2026The second order derivative of ⁻¹(4x^3 - 3x) with respect to ⁻¹(2x^2 - 1) , where 1 2 < x < 1 is 2026If 2 ⁻¹x - 3 ⁻¹x = 4 , then 2 ⁻¹x + 3 ⁻¹x = 2026 Full Inverse Trigonometric Functions list All AP EAMCET PYQs