⁻¹ (2 (2 cosec ⁻¹( 2 ) ) )=

Step-by-step solution

To evaluate ⁻¹ (2 (2 ⁻¹( 2 ) ) ) , begin with the innermost term ⁻¹( 2 ) , which has principal value 4 since ( 4 ) = 2 . Substituting gives 2 ⁻¹( 2 ) = 2 4 = 2 . Then ( 2 ) = 0 , so the argument becomes 2 0 = 0 . Finally, ⁻¹(0) = 2 , as ( 2 ) = 0 within the principal range. Final answer: 2