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If cos(tan-1x+cot-13) = 0, then value of x is ______. - Mathematics

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प्रश्न

If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.

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उत्तर

If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is `sqrt(3)`.

Explanation:

We have, `cos(tan^-1x + cot^-1 sqrt(3))` = 0

⇒ `tan^-1x + cot^-1  sqrt(3) = cos^-1 0`

⇒ `tan^-1x + cot^-1 sqrt(3) = pi/2`

⇒ `tan^-1x = pi/2 - cot^-1 sqrt(3)`

⇒ `tan^-1x = tan^-1 sqrt3)`  .....`(because tan^-1x + cot^-1x = pi/2)`

∴ x = `sqrt(3)`

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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 40 | पृष्ठ ४०

संबंधित प्रश्न

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