Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsInverse Trigonometric Functions

sin tan - 1 4 5 + tan - 1 4 3 + tan - 1 1 9 - tan - 1 1 7 =

Options

  1. A1 2
  2. B1 2
  3. C3 2
  4. D1

Correct answer

D. 1

Step-by-step solution

sin tan - 1 4 5 + tan - 1 4 3 + tan - 1 1 9 - tan - 1 1 7 = sin tan - 1 4 5 - tan - 1 1 7 + tan - 1 4 3 + tan - 1 1 9 Now, tan - 1 4 5 - tan - 1 1 7 = p say ⇒ p = tan - 1 4 5 - 1 7 1 + 4 5 · 1 7 = tan - 1 23 39 Also, tan - 1 4 3 + tan - 1 1 9 = q say ⇒ q = tan - 1 4 3 + 1 9 1 - 4 3 · 1 9 = tan - 1 39 23 ⇒ q = cot - 1 23 39 = π 2 - tan - 1 23 39 So, sin p + q = sin π 2 = 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 99 Percentile Qs Bank for JEE Main PYQs