Let cos⁻¹(1/2) = ϕ
cos(ϕ) = 1/2
ϕ = 60° or ϕ = 300°
Let y = sin[sin⁻¹(1) + cos⁻¹(1/2)]
y = sin(θ + ϕ)
y = sin(90° + 60°) or y = sin(90° + 300°)
y = sin(150°) or y = sin(390°)
y = sin(180° - 30°) or y = sin(360° - 30)
y = sin(30°)
y = 1/2
Sin[ sin^-1 1+ cos^-1 1/2)
expand it sin (sin^-1 1) cos(cos^-1 1/2) + sin (cos^-1 1/2) cos (sin^-1 1)=1/2+ sin 60 cos 90
=1/2, cos 60 =1/2, 60=cos^-1 (1/2), sin 90=1
90= sin^-1 1