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explain solution RD Sharma class 12 chapter Inverse Trignometric Functions exercise 3.7 question 2 sub question (vi) maths

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Answer:   2\pi -4

Hint: The principal value branch of function \cos ^{-1} is \left [ 0,\pi \right ]
Given: \cos ^{-1}(\cos 4)


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

And herex=4  which do not lie in the above range

            \begin{aligned} &\cos (2 \pi-x)=\cos (x) \\ &\cos (2 \pi-4)=\cos (4) \operatorname{so} 2 \pi-4 \text { belongs in }[0, \pi] \\ &\cos ^{-1}(\cos 4)=2 \pi-4 \end{aligned}



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