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If tan^(-1)a+tan^(-1)b+tan^(-1)c=pi then...

If `tan^(-1)a+tan^(-1)b+tan^(-1)c=pi` then prove tjhat `a+b+c=abc`

A

a+b+c=abc

B

ab+bc+ca=abc

C

`(1)/(a)+(1)/(b)+(1)/(c )-(1)/(abc)=0`

D

`ab+bc+ca=a+b+c`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
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  2. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

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

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  4. If a(1),a(2),a(3),….a(n) is a.p with common difference d then tan{tan...

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

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  6. Which of the following angles is greater? theta1=sin^(-1)(4/5)+sin^(-...

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

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  8. Solve tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1)"\ "8/(31)

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

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

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  11. Show that: cos(2tan^(-1)1/7)=sin(4^(-1)1/3)

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  12. Number of integral solutions of the equation 2 sin^-1sqrt(x^2-x +1 )+ ...

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  13. cos{cos^(-1)(-1/7)+sin^(-1)(-1/7)} =

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  14. If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal ...

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  15. sin[1/2cos^(- 1)4/5]

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  16. lf x >=0 and theta = sin^(-1)x + cos^(-1)x-tan^(-1) x, then

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  17. If tan^(-1)a+tan^(-1)b+tan^(-1)c=pi then prove tjhat a+b+c=abc

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  18. The value of cot(c o s e c^(- 1)5/3+tan^(- 1)(2/3))i s

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  19. Prove the following : sin^(-1)4/5+2\ tan^(-1)1/3=pi/2

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  20. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

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