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If X > 1, Then Write the Value of Sin−1 `((2x)/(1+X^2))` In Terms of Tan−1 X. - Mathematics

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Question

If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.

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Solution

sin`((2x)/(1+x^2))`

= π - 2 tan-1 x      `[because2tan^-1x=pi-sin^-1((2x)/(1+x^2))  "for"  x>1]`

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Chapter 4: Inverse Trigonometric Functions - Exercise 4.15 [Page 117]

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RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.15 | Q 4 | Page 117

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