If θ∈[4π,5π], then cos−1⁡(cos⁡θ) equals

If $θ \in [4 π, 5 π],$ then $\cos^{- 1} (\cos θ)$ equals

A
$- 4 π + θ$
B
$5 π - θ$
C
$4 π - θ$
D
$θ - 5 π$

Solution:

We have,

$θ \in [4 π, 5 π] \Rightarrow - 4 π + θ \in [0, π]$

Also,

$\begin{array}{l} \cos (- 4 π + θ) = \cos (4 π - θ) = \cos θ \\ ∴ \cos^{- 1} (\cos θ) = \cos^{- 1} {\cos (- 4 π + θ) ξ = - 4 π + θ \end{array}$

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