NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The number of integers for which the equation sin - 1 ⁡ x + cos - 1 ⁡ x + tan - 1 ⁡ x = n has real solution(s) is

Options

Correct answer

C. 2

Step-by-step solution

Given equation is π 2 + tan - 1 ⁡ x = n , ∀ x ∈ [ - 1 , 1 ] Now LHS ∈ π 4 , 3 π 4 Integers in this interval are 1 & 2 Hence, there are 2 integers for which the equation has real solutions

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 2026 Let = 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 2026 If ( ⁻¹(x 2 )) = ( ⁻¹ 1-x^2 ) , x (0,1) , then the value of x is : 2026 Let [ ] denote the greatest integer function. If the domain of the function f(x) = ⁻¹ ( x+[x] 3 ) is [ , ) , then ^2 + ^2 is equal to: 2026 Let 0 < < 1 , = 1 3 and ⁻¹(1- ) + ⁻¹(1- ) = 4 . Then 6( + ) is equal to: 2026 If 4 + _ p=1 ¹¹ ⁻¹ ( 2^ p-1 1 + 2^ 2p-1 ) = , then is equal to __________. 2026 If 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: 2026 Considering 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