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If |a|lt1|b|lt1and|x|lt1 then the soluti...

If `|a|lt1|b|lt1and|x|lt1` then the solution of `sin^(-1)((2a)/(1+a^(2)))-scos^(-1)(1-b^(2))/(1+b^(2))=tan^(-1)(2x)/(1-x^(2))` is

A

a

B

b

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Given,
`sin^(-1)""(2a)/(1+a^(2))-cos^(-1)""(1-b^(2))/(1+b^(2))`
`=tan^(-1)""(2x)/(1-x^(2))`
`implies1tan ^(-1)a-2tan^(-1)b=2 tan^(-1)x`
`impliestan ^(-1)((a-b)/(1+ab))=tan^(-1)x`
`impliesx=(a-b)/(1+ab)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 18-PAPER 2 (MATHEMATICS)
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  4. Which of the following is not a proposition ?

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  8. The probability that in the toss of two dice, we obtain the sum 7 or 1...

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  9. int(x^(e-1)+e^(x-1))/(x^(e)+e^(x)) dx is equal to

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  11. lim(n to oo) ((1)/(n)+(1)/(n+1)+...+(1)/(3n)) is equal to

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  12. lim(x to 0)((x)/(sqrt(1+x)-sqrt(1-x))) is equal to

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  13. The equations 2x-3y+6z=4, 5x+7y-14z=1 3x+2y-4z=0, have

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  14. The equation of the plane containing the two lines (x-1)/2=(y+1)/(-1...

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  15. If 2 tan ^(-1)(cos x )=tan ^(-1)(2 cosec x), then the value of x is

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  16. The value of int(2x+2)/((x-2)^(2)(x-3))dx is

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  17. Find the intervals in which the function f(x)=log(1+x)-(2x)/(2+x) is i...

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  18. The equation to the perpendicular from the point (alpha, beta gamma) t...

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  19. The solution of the differential equation (dy)/(dx)-y tan x=e^(x)sec x...

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  20. The value of int (0)^(pi//2)(sin ^(2)x-cos ^(2)x)/(sin ^(3)x+cos^(3)x...

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