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Show that , cos^(-1) 4/5 + cot^(-1) 5...

Show that , `cos^(-1) ` `4/5 `+ `cot^(-1) ` `5/3 ` = `tan^(-1) ` `27/11`

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UNITED BOOK HOUSE-SET 4-EXERCISE
  1. If vec a,vec b are two vectors such that vec a.vec b <0 and |vec a.ve...

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  2. If the straight line (x-11)/3=(y-2)/m=(z+3)/-2 is parallel to the plan...

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  3. Show that , cos^(-1) 4/5 + cot^(-1) 5/3 = tan^(-1) 27/11

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  4. answer any one question A=[[1,0],[-1,7]] and I be the unit matrix of s...

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  5. Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

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  6. f(x) = {(|x+1|/(x+1),when x!= -1),(0, when x = -1):} Test whether f(...

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  7. Find the value of c that occurs in the conclusion of lagrange's MVT in...

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  8. Solve: (x-y)(dx+dy) = dx-dy when x= 0, y = -1

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  9. For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|...

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  10. Show that the condition for the lines x= a1z+b1,y = c1z+d1 and x = a2z...

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  11. Can the two events A and B be mutually exclusive if P(A) = 1/8,P(A//B)...

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  12. Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in ...

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  13. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

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  14. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  15. Prove that |[x,a,b],[a,x,b],[a,b,x]|=(x-a)(x-b)(x+a+b)

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  16. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  17. If y = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sq...

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  18. If (sqrt(1-x^2))y= sin^(-1)x then show that (1-x^2)y2-3xy1-y =0

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  19. Evaluate: int(sin^(-1)x)/(1-x^2)^(3//2)dx

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  20. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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