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Please solve RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 2 sub question (vii) maths textbook solution

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Answer:   {2\pi }-5

Hint: The principal value branch of function \cos ^{-1} is \left [ 0,\pi \right ]
Given: \cos ^{-1}(\cos 5)


We know that \cos ^{-1}(\cos x)=x \text { if } x \in[0, \pi] \approx[0,3.14]

And here x=5  which do not lie in the above range.

We know that  \cos (2 \pi-x)=\cos (x)

            \cos (2 \pi-5)=\cos (5) \operatorname{so} 2 \pi-5 \text { belongs in }[0, \pi]

Hence,  \cos ^{-1}(\cos 5)=2 \pi-5


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