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Question: If \(\pi \leq x \leq 2 \pi\), then \(\cos ^ { - 1 } ( \cos x )\)is equal to....

If π≤x≤2π\pi \leq x \leq 2 \pi, then cos⁡−1(cos⁡x)\cos ^ { - 1 } ( \cos x )is equal to.

A

x

B

−x- x

C

2π+x2 \pi + x

D

2π−x2 \pi - x

Answer

2π−x2 \pi - x

Explanation

Solution

It is given that π≤x≤2π\pi \leq x \leq 2 \pi

⇒−π≥−x≥−2π⇒π≥2π−x≥0\Rightarrow - \pi \geq - x \geq - 2 \pi \Rightarrow \pi \geq 2 \pi - x \geq 0

⇒cos⁡−1{cos⁡(2π−x)}=2π−x\Rightarrow \cos ^ { - 1 } \{ \cos ( 2 \pi - x ) \} = 2 \pi - x.