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Solve the Following Equation For X: `Cos^-1((X^2-1)/(X^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3` - Mathematics

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प्रश्न

Solve the following equation for x:

`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`

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उत्तर

`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`

`=>cos^-1((1-x^2)/(1+x^2))+1/2xx2tan^-1x=(2x)/3`   `[becausetan^-1((2x)/(1-x^2))=2tan^-1x]`

`=>2tan^-1x+tan^-1x=(2x)/3`     `[becausecot^-1((1-x^2)/(1+x^2))=2tan^-1x]`

`=>3tan^-1x=(2x)/3`

`=>tan^-1x=(2x)/9`

`=>x=tan((2x)/9)`

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अध्याय 4: Inverse Trigonometric Functions - Exercise 4.14 [पृष्ठ ११६]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 4 Inverse Trigonometric Functions
Exercise 4.14 | Q 8.5 | पृष्ठ ११६

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