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If siny = x sin(a+y) then show that (dy)...

If `siny = x sin(a+y)` then show that `(dy)/(dx)= (sina)/(1-2xcos a+x^2)`.

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UNITED BOOK HOUSE-SET 15-EXERCISE
  1. Prove that, [[1+x,1,1],[1,1+y,1],[1,1,1+z]] = xyz(1 + 1/x+1/y+1/z)

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  2. Solve :[[x-2,2x-3,3x-4],[x-4,2x-9,3x-16],[x-8,2x-27,3x-64]]=0

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  3. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  4. Evaluate:int e^(4x)sin 3x dx

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  5. Evaluate:int (tan theta d theta)/(1-sin theta)

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  6. Solve:(x+y+1)dx + (2x+2y-1)dy = 0

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  7. solve:(dy)/(dx) + (sin 2y)/(x) = x^3cos^2y.

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  8. If the vectors a hati + hatj + hatk, hati + b hatj + hatk and hati + h...

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  11. find the value of underset(2)overset(3)int a^x dx(a<0).

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  12. Two cards are drawn successively with replacement from a well-shuffled...

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  13. Find the maximum value of f(x)=(1/x)^x

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  14. Solve: xdx+ ydy+ (xdy-ydx)/(x^2+y^2)=0 given y = 1 when x= 1.

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  15. Find the equation of the plane which contains the two parallel line: (...

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  16. A and B are two independent events such that P(AuuB) = 0.8 and P(A) = ...

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  17. vec a,vecb, vec c are three mutually perpendicular unit vectors then |...

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  18. The value of x if tan^(-1)x + 2 cot^(-1)x = (2 pi)/3 is

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  19. The degree of the differential equation(d^3y)/(dx^3) + x((dy)/(dx))^4 ...

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  20. If f(x) = [x] and g(x)=|x| the value of f(g(8/5))-g(f(-8/5)) is

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