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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

`(b)/(1+ab)`

C

`(b)/(1-ab)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Exercise
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  2. The value of tan[1/2cos^(-1).sqrt5/3] is

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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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  4. The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx) -sqr...

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  5. The value of sin[cot^(-1){cos(tan^(-1) x)}] is

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  6. If x >1 , then 2\ tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is equal to 4tan^(-...

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  7. If A=tan^-1((xsqrt3)/(2k-x)) and B=tan^-1((2x-k)/(ksqrt3)) then find t...

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  8. If sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x then x equals

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  9. If -1 le x le 0 then cos^(-1)(2x^(2)-1) equals

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  10. If -1/2 le x le 1/2 hence sin^(-1)(3x-4x^(3)) equals

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  11. The value of sin^(-1)(sin 10) is

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  12. The value of tan^(-1)1+tan^(-1)2+tan^(-1)3 is

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  13. The value of sin^(-1)[cos((33pi)/5)] is

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  14. Find the smallest and the largest values of tan^(-1) ((1 - x)/(1 + x))...

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  15. The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (...

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  16. If a le 1/32 then the number of solution of (sin^(-1) x)^(3) +(cos^(...

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  17. If x takes negative permissible vlaue then sin^(-1)x=

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  18. If -1 le x le -(1)/sqrt(2) then sin^(-1)2xsqrt(1-x^(2)) equals

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  19. If (1)/sqrt(2) le x le 1 then sin^(-1) 2xsqrt(1-x^(2)) equals

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