Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201910 Jan 2019Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The value of cot ⁡ ∑ n = 1 19 cot - 1 ⁡ 1 + ∑ p = 1 n 2 p is:

Options

  1. A21 19
  2. B19 21
  3. C23 22
  4. D22 23

Correct answer

A. 21 19

Step-by-step solution

We have, cot ⁡ ∑ n = 1 19 cot - 1 ⁡ 1 + ∑ p = 1 n 2 p = c o t ∑ n = 1 19 t a n - 1 1 1 + n n + 1 = c o t ∑ n = 1 19 t a n - 1 n + 1 - n 1 + n n + 1 = c o t ⁡ ∑ n = 1 19 ( t a n - 1 n + 1 - t a n - 1 n ) = cot ⁡ t a n - 1 20 - t a n - 1 1 = 1 t a n ( t a n - 1 20 - t a n - 1 1 ) = 1 20 - 1 1 + ( 20 ) . 1 = 21 19

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 JEE Main PYQs