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  • need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 4 sub question (i)

need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 4 sub question (i)

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Answer: \frac{\pi }{3}

Hint: The range of principal value of  \sec ^{-1}  is  \hspace{0.2cm}\forall x\in[0,\pi]\hspace{0.2cm},x\neq \frac{\pi}{2}
Given:  \sec ^{-1}\left(\sec \frac{\pi}{3}\right)

Explanation:

As        \sec ^{-1}(\sec x)=x \text { if } x \in[0, \pi]-\left\{\frac{\pi}{2}\right\}

By applying this situation we get,

            \sec ^{-1}\left(\sec \frac{\pi}{3}\right)=\frac{\pi}{3}

Hence,  \sec ^{-1}\left(\sec \frac{\pi}{3}\right)=\frac{\pi}{3}

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