If ⁻¹ [ 5-2 6 1+ 6 ] = 3 - ⁻¹(k) , then ⁻¹(k) = ...

Step-by-step solution

Simplify the expression inside the inverse tangent function: 5-2 6 = 3 + 2 - 2 3 2 = ( 3 - 2 )^2 = 3 - 2 Substitute this back into the given equation: ⁻¹ [ 5-2 6 1+ 6 ] = ⁻¹ [ 3 - 2 1+ 3 2 ] Using the identity ⁻¹ ( x-y 1+xy ) = ⁻¹(x) - ⁻¹(y) , we get: ⁻¹ [ 3 - 2 1+ 3 2 ] = ⁻¹( 3 ) - ⁻¹( 2 ) Since ⁻¹( 3 ) = 3 , the expression becomes: 3 - ⁻¹( 2 ) Equating this to the given right-hand side: 3 - ⁻¹( 2 ) = 3 - ⁻¹(k) k = 2 Now, find the value of ⁻¹(k) : ⁻¹( 2 ) = 4 Answer: 4