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If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-...

If `alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)))` then prove that `x^(2) = sin 2alpha`.

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AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 7.1 ( SHORT ANSWER QUESTIONS)
  1. Prove that 2sin^-1(3/5)-Cos^-1""5/13=Cos^-1(323/325).

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  2. Prove that "Sin"^(-1)4/52"+Tan"^(-1)1/3=(pi)/2

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  3. If alpha = Tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2)...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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