The value of an inverse trigonometric functions which lies in its principal value branch is called the  –coscoseccotprincipal valuesecsinsinxsinyx of that inverse trigonometric functions.

y=sin⁻¹x⇒ x =  –coscoseccotprincipal valuesecsinsinxsinyx

sin (sin⁻¹x) =  –coscoseccotprincipal valuesecsinsinxsinyx.

sin⁻¹( –coscoseccotprincipal valuesecsinsinxsinyx) = x

sin⁻¹(¹⁄ₓ)=  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x

cos⁻¹(–x) = π –  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x

cos⁻¹(¹⁄ₓ) =  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x

cot⁻¹(–x) = π –  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x

tan⁻¹(¹⁄ₓ)=  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x.

sin⁻¹(–x) =  –coscoseccotprincipal valuesecsinsinxsinyx sin⁻¹x

tan⁻¹x +  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x = π/2

sin⁻¹x +  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x = π⁄2

cosec⁻¹x +  –coscoseccotprincipal valuesecsinsinxsinyx⁻¹x = π/2

x =  –coscoseccotprincipal valuesecsinsinxsinyxy ⇒ y = sin⁻¹x