Evaluate each of the following:

(i)`cos^(-1)(cos5)`

(ii) `cos^(-1)(cos12)`

Explanation

(i) We know,

`\cos ^{-1}(\cos \theta)=\theta \text { if }(0 \leq \theta \leq \pi) `

`\cos (2 \pi-\theta)=\cos \theta`

We have


`\cos ^{-1}(\cos 5)=\cos ^{-1}\{\cos (2 \pi-5)\} \quad \text { Where, } 0 \leq 2 \pi-5 \leq \pi`

`=2 \pi-5`

`\therefore \cos ^{-1}(\cos 5)=2 \pi-5`

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