Question

`cos^(-1) (cos  (7pi)/6)` is equal to ______.

Options

• `(7pi)/6`

• `(5pi)/6`

• `pi/3`

• `pi/6`

Answer 1

`cos^(-1) (cos  (7pi)/6)` is equal to `underlinebb((5pi)/6)`.

Explanation:

`cos^(-1) (cos  (7pi)/6) ≠ (7pi)/6` as the principal value branch of cos^–1 is [0, π].

∴ `cos^(-1) (cos  (7pi)/6)`

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

= `cos^-1(-cos  pi/6)`

= `cos^-1 (cos(pi - pi/6))`

= `(5pi)/6`