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Prove that tan^(-1)sqrt(x) =(1)/(2) cos^...

Prove that `tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)`.

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SHARAM PUBLICATION-MODEL QUESTION PAPER 13-EXERCISE
  1. Write the intercepts cutoff by the plane 2x+y-z =5 on three axes.

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  2. Show that the relation S in set A={x in Z : 0 le x le 12} given by S=...

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  3. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  4. Solve: sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x.

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  5. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  6. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

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  7. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  8. Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^...

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  9. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  10. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  11. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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  12. If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2.

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  13. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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  14. Find the points on the curve x^(2) + y^(2) - 2x - 3 = 0 at which the t...

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  15. For which value of x, the function f(x)=4-x-x^2is maximum or minimum.

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  16. Evaluate int (x+3)^2dx

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  17. Evaluateint0^pi (2/4)sinsqrtxdx

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  18. Evaluate int sin^-1 x dx

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  19. Find the area bounded by the line y = 2x, x- axis and the ordinate x =...

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  20. Solve(dy)/(dt)=e^(3t+5y)

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