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If |x| le 1, then 2tan^(-1)x + sin^(-1)...

If `|x| le 1`, then ` 2tan^(-1)x + sin^(-1)((2x)/(1+x^(2)))` is equal to

A

`4 tan^(-1)x`

B

`0`

C

`pi/2`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `2tan^(-1) x + sin^(-1)'(2x)/(1+x^(2))`
Let `x = tantheta`
`:. 2tan^(-1) tantheta + sin^(-1)'(2tan theta)/(1+tan^(2)theta) , [:' tan^(-1)(tanx) = 4]`
`= 2 theta + sin^(-1) sin2theta , [:' sin 2 theta = (2tan theta)/(1+tan^(2)theta)]`
`= 2theta +sin^(-1)sin 2theta , [:' sin^(-1)(sinx) = x]`
`= 4 theta , [:' theta = tan^(-1)x]`
`= 4 tan^(-1)x`
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NCERT EXEMPLAR-INVERSE TRIGONOMETRIC FUNCTIONS-Inverse Trigonometric Functions
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  13. The value of cos(sin^(-1)x + cos^(-1)x), where |x| le 1, is

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  14. The value of tan((sin^(-1)x+cos^(-1)x)/(2)), when x = (sqrt(3))/(2), i...

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  15. If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))), then "………"lt y lt "………".

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  16. The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true whe...

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