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The value of cos-1(cos 14π3) is ______. - Mathematics

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प्रश्न

The value of `cos^-1 (cos  (14pi)/3)` is ______.

रिक्त स्थान भरें
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उत्तर

The value of `cos^-1 (cos  (14pi)/3)` is `(2pi)/3`.

Explanation:

`cos^-1 (cos  (14pi)/3) ≠ (14pi)/3` as `(14pi)/3 ∉ [0, pi]`

∴  `cos^-1 (cos  (14pi)/3) = cos^-1 cos(4pi + (2pi)/3)`

= `cos^-1 cos  (2pi)/3`  .....`(because cos(2"n"pi + theta) = cos theta)`

= `(2pi)/3`   ......`(because cos^-1 (cos x) = x, x ∈ [0, pi])`

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अध्याय 2: Inverse Trigonometric Functions - Exercise [पृष्ठ ४०]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 2 Inverse Trigonometric Functions
Exercise | Q 43 | पृष्ठ ४०

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