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provide solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise  3.7 question 2 sub question (viii)

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Answer:   {4\pi }-12

Hint: The principal value branch of function \cos ^{-1} is \left [ 0,\pi \right ]
Given: \cos ^{-1}(\cos 12)


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

Herex=12  which do not lie in the above range.

We know that

            \begin{aligned} &\cos (2 n \pi-x)=\cos (x) \\ &\cos (2 n \pi-12)=\cos 12 \end{aligned}

Here,    n=2

Also,    \begin{aligned} &4 \pi-12 \text { belongs in }[0, \pi] \end{aligned}

            \cos ^{-1}(\cos 12)=4 \pi-12

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