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

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

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UNITED BOOK HOUSE-SET 2-EXERCISE
  1. The probability of getting 11 when an ordinary die is thrown twice is

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  2. If in a biomial distribution n=4, P(x=0) = 16/81 then the value of P(x...

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

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  4. Evaluate: |[1,a,bc],[1,b,ca],[1,c,ab]|

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  5. Show that function f(x) = 2x-|x| is continous at x=0.

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  6. Evaluate: overset(2)underset(1)int logx dx

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  7. Find the order of the differential equation ((d^4y)/(dx^4))^3-(d^3y...

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  8. Prove that the function f(x) = x+1/x(x!=0) is decreasing for all x in ...

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  9. Determine the area bounded by rectangular hyperbola xy=c^2 the x-axis ...

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  10. The direction agnles of a straight line are 120^@,45^@,30^@. Is the s...

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  11. Find K, for which the two planes x+ky+5z+2=0 and 3x-2y+kz-1=0 are perp...

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  12. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  13. Find the probability of guessing correctly at least 5 of the eight ans...

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  14. Solve: tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)= tan^(-1)3x.

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  15. If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that...

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  16. If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such t...

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  17. Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c...

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  18. If x^2+y^2= t-1/t and x^4+y^4 = t^2+1/t^2,show that , x^3y (dy)/(dx) =...

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  19. If 2x= y^(1/5)+y^(-1/5) prove that (x^2-1)y2+xy1 = 25y

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  20. Solve: (2x+4y+3)(dy)/(dx)= 2y+x+1

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