Write the value of sin-1(\(-\frac{\sqrt3}2\)) + cos-1(\(-\frac 12\))

1.	Write the value of sin-1(\(-\frac{\sqrt3}2\)) + cos-1(\(-\frac 12\))
Answer» Let sin^-1(-√3/2) = x and cos^-1(-1/2) = ⇒ sin x = (-√3/ 2) and cos y = -1/2 We know that the range of the principal value branch of sin^-1is (-π/2, π/2) and cos^-1 is (0, π). We also know that sin (-π/ 3) = (-√3/ 2) and cos (2π/3) = -1/2 ∴ Value of sin^-1 (-√3 /2) + cos^-1(-1/2) = -π/3 + 2π/3 = π/3

Answer»

Let sin^-1(-√3/2) = x and cos^-1(-1/2) =

⇒ sin x = (-√3/ 2) and cos y = -1/2

We know that the range of the principal value branch of sin^-1is (-π/2, π/2) and cos^-1 is (0, π).

We also know that sin (-π/ 3) = (-√3/ 2) and cos (2π/3) = -1/2

∴ Value of sin^-1 (-√3 /2) + cos^-1(-1/2) = -π/3 + 2π/3

= π/3

Discussion