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Question
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
Options
`4 tan^-1x`
0
`pi/2`
π
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Solution
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to `4 tan^-1x`.
Explanation:
Here, we have `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))`
= `2tan^-1x + 2tan^-1x` ....`[because 2 tan^-1x = sin^-1 (2x)/(1 + x^2)]`
= 4 tan–1x
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