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If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2...

If `sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x` then `x=`

A

`(a-b)/(1+ab)`

B

`(a-b)/(1-ab)`

C

`(2ab)/(1+ab)`

D

`(a+b)/(1-ab)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since a `gt` 0, b `gt` 0 and 2 `tan^(-1)x=sin^(-1)((2x)/(1+x^(2)))`
`therefore` Given expression is `2 tan^(-1) a + 2 tan^(-1) b = 2 tan^(-1) x`
`rArr 2 tan^(-1)((a+b)/(1-ab))=2 tan^(-1)x`
`rArr x = (a+b)/(1-ab)`
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NDA PREVIOUS YEARS-PROPERTIES OF TRIANGLE, INVERSE TRIGONOMETRIC FUNCTION-MCQ
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  2. In any triangle ABC, if a=\ 18 , b=\ 24 , c=\ 30, findsinA, sinB, sinC

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  3. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

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  6. If x and y are positive and xygt1, then what is tan^(-1)x+tan^(-1)y to...

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  7. Consider the following statement : 1. There exixts no triangle ABC f...

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  8. Consider the following statement : 1. tan^(-1)1 + tan^(-1) (0.5) = p...

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  9. If A + B + C = pi, then what is cos(A + B) + cos C equal to ?

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  10. What is sin^(-1)"sin"(3 pi)/(5) equal to ?

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  11. What is "sin"^(-1)(3)/(5)- "sin"^(-1)(4)/(5) equal to ?

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  12. In a triangle ABC, c = 2, A = 45^(@), a = 2 sqrt(2), than what is C eq...

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  13. In a triangle ABC, sin A- cos B = Cos C, then angle B is

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  14. If in triangle ABC, (a=(1+sqrt(3))c m ,b=2c m ,a n d/C=60^0 , then fin...

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  15. A solution of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(2) is

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  16. Conisder x = 4 tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1...

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  17. Conisder x = 4 tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1...

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  18. Conisder x = 4 tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1...

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  19. The value of tan (2 "tan"^(-1)(1)/(5)-(pi)/(4)) is

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  20. Consider the following statements : 1. sin^(-1)\ 4/5 + sin^(-1)\ 3/5...

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