The value of [2 ⁻¹ 1 5 - 4 ] is

Step-by-step solution

To evaluate [2 ⁻¹ 1 5 - 4 ] , begin by simplifying 2 ⁻¹ 1 5 using the identity 2 ⁻¹x = ⁻¹ ( 2x 1-x^2 ) . With x = 1 5 , this becomes ⁻¹ ( 2 1 5 1- ( 1 5 )^2 ) = ⁻¹ ( 2 5 24 25 ) = ⁻¹ ( 5 12 ) . The expression is thus [ ⁻¹ 5 12 - 4 ] . Applying the tangent subtraction formula, (A-B) = A - B 1 + A B , where A = ⁻¹ 5 12 and B = 4 , yields A = 5 12 and B = 1 . Substituting gives 5 12 - 1 1 + 5 12 1 = - 7 12 17 12 = - 7 17 . Among the options, C is correct.