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  • need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 5 sub question (i)

need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 5sub question (i)

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Answer: \frac{\pi }{4}

Hint: The range of principal value of  \operatorname{cosec}^{-1} \text { is }\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}
Given:  \operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{\pi}{4}\right)

Explanation:

As we know,

            \operatorname{cosec}^{-1}(\operatorname{cosec} x)=x \text { when } x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}

By applying this situation we get,

            \operatorname{cosec}^{-1}\left(\operatorname{cosec} \frac{\pi}{4}\right)=\frac{\pi}{4}

 

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