The value of ⁻¹ (- 1 2 )+ ⁻¹ (- 1 2 )- ⁻¹ (- 1 3 )+ ⁻¹(+ 3 )

Step-by-step solution

Let E = ⁻¹ (- 1 2 ) + ⁻¹ (- 1 2 ) - ⁻¹ (- 1 3 ) + ⁻¹( 3 ) . Using principal value ranges: ⁻¹ (- 1 2 ) = - 4 ⁻¹ (- 1 2 ) = 2 3 ⁻¹ (- 1 3 ) = - ⁻¹ ( 1 3 ) = - 3 = 2 3 ⁻¹( 3 ) = 3 Substituting yields: E = - 4 + 2 3 - 2 3 + 3 = - 4 + 3 Combining terms with common denominator 12: E = - 3 12 + 4 12 = 12 12