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Find the sum of infinite series s = si...

Find the sum of infinite series
`s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ((sqrt2 -1)/sqrt6) + sin ^(-1) ((sqrt3 - sqrt2)/(2sqrt3)) + ...+ sin^(-1) ((sqrtn - sqrt(n-1))/(sqrt(n(n+1))))+... infty`

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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/4

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  3. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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

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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. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  13. Thee value of cos ^(−1 )x+cos ^(−1)( x/2​ + root(3-x^2)/2−x2 ​ ), wh...

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

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  15. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

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

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

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  18. The trigonometric equation sin^(-1) x = 2 sin^(-1) a has a solution fo...

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  19. If cos^(-1) x - cos^(-1).(y)/(2) = alpha, then 4x^(2) - 4xy cos alpha ...

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

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