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Find the Principal Value of the Following: `Sec^-1(2)` - Mathematics

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प्रश्न

Find the principal value of the following:

`sec^-1(2)`

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उत्तर

Let `sec^-1(2)=y`
Then,
sec y = 2
We know that the range of the principal value branch is `[0,pi]-{pi/2}.`
Thus,
`secy=2=sec(pi/3)`

`=>y=pi/3in[0,pi],y!=pi/2`

Hence, the principal value of `sec^-1(2)   is    pi/3. `

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अध्याय 4: Inverse Trigonometric Functions - Exercise 4.04 [पृष्ठ १८]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 4 Inverse Trigonometric Functions
Exercise 4.04 | Q 1.2 | पृष्ठ १८

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