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The sum of the infinte series sin^(-1)(1...

The sum of the infinte series `sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+....sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))`

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The sum of the infinite series "sin"^(-1)((1)/(sqrt2))+"sin"^(-1)((sqrt2-1)/(sqrt6))+"sin"^(-1)((sqrt3-sqrt2)/(sqrt12))+…+…+"sin"^(-1)((sqrtn-sqrt((n-1)))/(sqrt(n(n+1))))+… is

Q.29 Find the sum of the series sin^(-1)((1)/(sqrt(5)))+sin^(-1)((1)/(sqrt(65)))cdots

The sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals

The sum of n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+... is

sin^(-1){cot(sin^(-1)(sqrt((2-sqrt(3))/(4))+cos^(-1)((sqrt(12))/(4))+sec^(-1)sqrt(2))}

The sum to n terms of the series (1)/(sqrt(7)+sqrt(10))+(1)/(sqrt(10)+sqrt(13))+(1)/(sqrt(13)+sqrt(16))+... is

For all n in N,1+(1)/(sqrt(2))+(1)/(sqrt(3))+(1)/(sqrt(4))++(1)/(sqrt(n))

sum_(n=1)^(oo)(1)/(sqrt(n)+sqrt(n+1))

lim_(n rarr oo)(sin(1)/(sqrt((n))))((1)/(sqrt(n+1)))^(+(1)/(sqrt(n+2))+(1)/(sqrt(n+2)))

The sum n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+sqrt(5))+(1)/(sqrt(5)+sqrt(7))+... is sqrt(2n+1) (b) (1)/(2)sqrt(2n+1)(c)(1)/(2)sqrt(2n+1)-1(d)(1)/(2){sqrt(2n+1)-1}

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that the identities, sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi...

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  2. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4m/n gt;-1(-3pi)/4m...

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  3. The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)...

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  4. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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  5. If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > ...

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  6. Solution set of inequality (cot^-1x)^2-5cot^-1x+6>0 is (A) (cot 3 ,...

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  7. Solve the following inequality: sin^(-1) x > cos^(-1) x

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  8. Solve the following system of inequations: 4(tan^(-1)x)^2-8tan^(-1)x+3...

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  9. Find the number of positive integral solution of the equation tan^(-1)...

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  10. Find all values of k for which there is a triangle whose angles have m...

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  11. Find the range of the function f(x)=(sin^(-1)x)^3+(cos^(-1)x)^3dot

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  12. Q.34 Q.34 Show that the roots r,s and t of the cubic Show that the roo...

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  13. The number of solutions of the equation |y|= cos x and y = cot^-1 (cot...

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  14. Solve for x : sin^(- 1)(sin((2x^2+4)/(1+x^2)))lt pi-3

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  15. Find the set of values of 'a' for which the equation 2cos^-1 x = a+a^2...

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  16. The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. ...

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  17. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  18. If cos^(- 1)x-cos^(- 1)(y/2)=alpha then 4x^2-4xycosalpha+y^2=

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  19. If sin^(-1)(x/5)+cose c^(-1)(5/4)=pi/2 then the value of x is: (1) ...

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  20. The value of cot(cose c^(-1)5/3+tan^(-1)2/3) is: (1) 6/(17) (2) 3/...

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