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

Step-by-step solution

aligned & ⁻¹( 3 )- ⁻¹(-2) cosec ⁻¹(- 2 )+ ⁻¹ ( -1 2 ) & = ⁻¹( 3 )- ⁻¹ ( -1 2 ) ⁻¹ ( -1 2 )+ ⁻¹ ( -1 2 ) aligned [ array l ⁻¹ x= ⁻¹ 1 x cosec ⁻¹ x= ⁻¹ 1 x array ]= ⁻¹( 3 )- + ⁻¹ ( 1 2 ) - ⁻¹ ( 1 2 )+ - ⁻¹ ( 1 2 ) [ array l ⁻¹(-x)= - ⁻¹ x ⁻¹(-x)=- ⁻¹ x array ] aligned & = 3 - + 3 - 4 + - 3 & = - 3 5 12 & = -4 5 aligned