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Show that cot(Sin^-1sqrt(13/17))=sin(Ta...

Show that `cot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3)`.

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AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 7.1 ( SHORT ANSWER QUESTIONS)
  1. Show that "sec"^(2)(Tan^(-1)2)+"cosec"^(2)(Cot^(-1)2) =10

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  2. Show that Sec^(2)(cot^(-1)3)+(Cosec^(2)(tan^(-1)2))=85/36

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  3. Show that cot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).

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  4. Show that cos(2"Tan"^(-1)1/7)=sin(4"Tan"^(-1)1/3)

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  5. sin(2"Tan"^(-1)3/4)=

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  6. Show that tan[2 tan^(-1)((sqrt(5)-1)/(2))]=2

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  7. "Tan"^(-1)1/4+"Tan"^(-1)2/9=

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  8. Prove that 2sin^-1(3/5)-Cos^-1""5/13=Cos^-1(323/325).

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

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

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

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

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

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

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

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

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

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

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