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Id a,b,c are distinct non-zero real numb...

Id `a,b,c` are distinct non-zero real numbers having the same sign. Prove that
`Cot^(-1)((ab+1)/(a-b)) +cot^(-1)((bc+1)/(b-c))+ Cot^(-1)((ca+1)/(c-a)) = pi (or) 2 pi`.

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AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 7.1 ( SHORT ANSWER QUESTIONS)
  1. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

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  2. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+y...

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  3. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  4. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  5. tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

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  6. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

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  7. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

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  8. Id a,b,c are distinct non-zero real numbers having the same sign. Prov...

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  9. solve the following equations cos(2sin^(-1)x)=1/9

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  10. solve the following equations tan(arc"cos"1/x)=sin(arc"cot"1/2),x!=0

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  11. If "Cos"^(-1)3/5-"Sin"^(-1)4/5=Cos^(-1)x then x =

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  12. If "Sin"^(-1)5/x+"Sin"^(-1)12/x=pi/2, then x =

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  13. solve the following equations sin^(-1)x+sin^(-1)2x=(pi)/3

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  14. Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 the...

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  15. solve the following equations Cot^(-1)((1+x)/(1-x))=1/2Cot^(-1)(1/x)...

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  16. solve the following equations Cos^(-1) (sqrt(3).x)+Cos^(-1)(x)=(pi)/...

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  17. If Sin^(-1)x-Cos^(-1)x = (pi)/6 then find x.

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  18. Solve 3Sin^(-1)((2x)/(1+x^(2))) - 4 Cos^(-1)((1-x^(2))/(1+x^(2)))+2Tan...

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  19. Solve the following equations "Tan"^(-1)(x-1)/(x-2)+"Tan"^(-1)(x+1)/...

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  20. If Sin^(-1)(2p)/(1+p^(2)) - Cos^(-1)((1-q^(2))/(1+q^(2))) = Tan^(-1) (...

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