The value of 2 ⁻¹ 1 2 + ⁻¹ 3 8 is

Step-by-step solution

Given expression: E = 2 ⁻¹ 1 2 + ⁻¹ 3 8 Using the identity for 2 ⁻¹ x = ⁻¹ ( 2x 1-x^2 ) where |x| 2 ⁻¹ 1 2 = ⁻¹ ( 2 1 2 1 - ( 1 2 )^2 ) = ⁻¹ ( 1 3 4 ) = ⁻¹ 4 3 Substituting back: E = ⁻¹ 4 3 + ⁻¹ 3 8 Apply addition formula for inverse tangent, ⁻¹ x + ⁻¹ y = ⁻¹ ( x+y 1-xy ) for xy Verify xy = 4 3 3 8 = 1 2 E = ⁻¹ ( 4 3 + 3 8 1 - 4 3 3 8 ) = ⁻¹ ( 41 24 1 2 ) = ⁻¹ ( 41 12 ) This matches option D: D