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Show that Sec^2 (cot^-1(2)) + cosec^2(ta...

Show that `Sec^2 (cot^-1(2)) + cosec^2(tan^-1 (3)) = 2 13/36`

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UNITED BOOK HOUSE-SET 18-EXERCISE
  1. Let us consider a function f : R rarrR, defined by f(x) =x^3 - 6. Show...

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  2. Show that Sec^2 (cot^-1(2)) + cosec^2(tan^-1 (3)) = 2 13/36

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  3. If A = [(3,-5),(-4,2)] then show that A+A' is a symmetric matrix.

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  4. Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x...

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  5. Examine the applicability of lagrange's Mean value theorem for the fun...

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  6. If sin^(-1) ((x^2-y^2)/(x^2+y^2))=k, k is a constant, then prove that ...

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  7. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

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  8. Using the method of differentail find the approximate value of sqrt 0....

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  9. If veca = 3hati - 2hatj + hatk and vecb = hati - 3hatj + hatk find vec...

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  10. If direction ratios of two lines are (a,b,c)and (b-c,c-a,a-b), find an...

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  11. Find the binomial distribution for which the mean and variance are 12 ...

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  12. If for two events A and B, P(A) = P(A/B) = 1/4 and P(B/A) = 1/2, show ...

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  13. if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then sho...

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  14. If A = [(1,0),(0,1)] and B = [(0,1),(-1,0)], show that (pA + qB) (pA -...

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  15. If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

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  16. Solve for x : |(x,a,b),(a,x,b),(a,b,x)| = 0

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  17. Find the derivation of sin^-1 (x^2 sqrt(1-x) - sqrtx sqrt(1-x^4)) with...

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  18. Evaluate : int(x^2dx)/((x sin x + cos x)^2)

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  19. Solve: (dy)/(dx) +x(sin2y) = x^3 cos^2 y, y(0) = then y(1) equal to

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  20. The temperature T of a cooling object drops at a rate proportional to ...

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