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Prove that : I(n)^(-1)=I(n)...

Prove that :
`I_(n)^(-1)=I_(n)`

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Prove that : adj. I_(n)=I_(n)

If I_(n)=int_(0)^(1)x^(n)(tan^(-1)x)dx, then prove that(n+1)I_(n)+(n-1)I_(n-2)=-(1)/(n)+(pi)/(2)

If I_n=int_0^ooe^(-x)x^(n-1)log_exdx , then prove that I_(n+2)-(2n+1)I_(n+1)+n^2I_n=0

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, prove that I_(n)+I_(n-2)=(1)/(n+1)

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_(n)=int_(0)^(1)(dx)/((1+x^(2))^(n));n in N, then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_(n)

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

If I_(n)=int x^(n)sqrt(a^(2)-x^(2))dx, prove that I_(n)=-(x^(n-1)(a^(2)-x^(2))^((3)/(2)))/((n+2))+((n+1))/((n+2))a^(2)I_(n-2)

i) If tan (A+B) = n tan (A-B), prove that: (n+1)/(n-1) = (sin2A)/(sin2B)

MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

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  2. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

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  3. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

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  4. If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

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  5. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

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  6. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

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  7. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

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  8. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

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  9. If A=[1tanx-tanx1] , show that A^T\ A^(-1)=[cos2x-sin2xsin2xcos2x] .

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  10. If A=[(2,-3),(4,6)] " verify that " (adj A)^(-1)=(adj A^(-1)).

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  11. Prove that : adj. I(n)=I(n)

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  12. Prove that : adj.O=O

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  13. Prove that : I(n)^(-1)=I(n)

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  14. Find the inverse of each of the matrices given below : Let D= "dia...

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  15. Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}...

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  16. Find the inverse of each of the matrices given below : Obtain the in...

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  17. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

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  18. If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of ...

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  19. Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integ...

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  20. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

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