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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)))-cos^(-1)((1-b^(2))/(1+b^(2)))=tan^(-1)((2x)/(1-x^(2)))` is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

We have
`sin^(-1)(2a)/(1+a^(2))-cos^(-1)(1-b^(2))/(1+b^(2))=tan^(-1)(2x)/(1-x^(2))`
`rarr 2tan^(-1)a-2tan^(-1)b=2tan^(-1)x`
`rarr tan^(-1)a-tan^(-1)b=tan^(-1)x`
`rarr tan^(-1)x=tan^(-1)(a-b)/(1+ab)`
`rarr x=(a-bb)/(1+ab)`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. If |a|lt1|b|lt1and|x|lt1 then the solution of sin^(-1)((2a)/(1+a^(2)))...

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  2. Solve sin^(-1)(1-x)-2sin ^(-1)x=pi/2

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  3. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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  4. If tantheta + tan(theta + pi/3) + tan(theta-pi/3)= Ktan3theta, then K ...

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  5. If -1 le x le -1/2, then sin^(-1)(3x-4x^3) equals

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  6. The numerical value of "tan"(2tan^(-1)(1/5)-pi/4 is equal to

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  7. If tan(x+y)=33, and x= tan^(-1)3, then: y=

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  8. Two angles of a triangle are cot^-1 2 and cot^-1 3, then the third ang...

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  9. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

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  10. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

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  11. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2) the value of x^(100)+y^(10...

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  12. The value of (alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1) ((alpha)/(bet...

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  13. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

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  14. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

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  15. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  16. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

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  17. Which of the following angles is greater? theta1=sin^(-1)+sin^(-1)1/3o...

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  18. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

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  19. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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  20. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

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  21. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

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