The value of ⁻¹ [ ( 1 2 ⁻¹ 1 3 + ⁻¹ 12 4 + ⁻¹ 1 2 ) ] is

Step-by-step solution

Let the expression inside the cotangent be . = 1 2 ⁻¹ ( 1 3 ) + ⁻¹ ( 12 4 ) + ⁻¹ ( 1 2 ) We know that ⁻¹ ( 1 3 ) = 6 . Also, 12 4 = 2 3 4 = 3 2 , so ⁻¹ ( 3 2 ) = 6 . And ⁻¹ ( 1 2 ) = 4 . Substituting these values into : = 1 2 ( 6 ) + 6 + 4 = 12 + 6 + 4 Finding a common denominator of 12: = + 2 + 3 12 = 6 12 = 2 The expression becomes ⁻¹ [ ( )] = ⁻¹ [ ( /2)] . Since ( /2) = 0 , we have ⁻¹(0) = 0 . Answer: 0