Question

Find the value of `cos^-1 (1/2) + 2sin^-1 (1/2) ->`:-

Options

• `(2pi)/3`

• `pi/3`

• `pi`

• 0

Answer 1

`(2pi)/3`

Explanation:

Let `cos^-1 (1/2)` = x

⇒ `cos x = 1/2 = cos (pi/3)`

∴ `cos^-1 (1/2) = pi/3`

Let `sin^-1 (1/2)` = y

⇒ `sin y = 1/2 = sin (pi/6)`

∴ `sin^-1 (1/2) = pi/6`

`cos^-1 (1/2) + 2sin^-1 (1/2) = pi/3 + (2pi)/6 + pi/3 + pi/3 = (2pi)/3`