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Find the Principal Value of the Following: `Cot^-1(Tan (3pi)/4)` - Mathematics

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प्रश्न

Find the principal value of the following:

`cot^-1(tan  (3pi)/4)`

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उत्तर

Let `cot^-1(tan  (3pi)/4) = y`

Then,

`coty=tan  (3pi)/4`

We know that the range of the principal value branch is (0, π).

Thus,

`coty=tan  (3pi)/4=-1=cot((3pi)/4)`

`=>y=(3pi)/4in(0,pi)`

Hence, the principal value of `cot^-1(tan  (3pi)/4)    is    (3pi)/4.`

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पाठ 4: Inverse Trigonometric Functions - Exercise 4.06 [पृष्ठ २४]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 4 Inverse Trigonometric Functions
Exercise 4.06 | Q 1.4 | पृष्ठ २४

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