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Solve - frac{sin^(3) frac{x}{2} -cos^(3)...

Solve - `frac{sin^(3) frac{x}{2} -cos^(3) frac{x}{2}}{2 +sinx} = cosx/3`

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A DAS GUPTA-Miscellaneous Exercises-Exercise
  1. Find the equations of straight lines which pass through the intersecti...

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  2. The circle x^2+y^2=1 cuts the x-axis at Pa n dQdot Another circle with...

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  3. Solve - frac{sin^(3) frac{x}{2} -cos^(3) frac{x}{2}}{2 +sinx} = cosx/3

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  4. let f(x) be the polynomial function. It satisfies the equation 2 +f(x)...

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  5. Evaluate int(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx.

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  6. Find the co-ordinates of all the points P on the ellipse, x^2/a^2+y^2/...

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  7. Find the equation of a curve passing through the point (1.1) if the pe...

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  8. Solve: (x^2 + 4y^2 + 4xy) dy = (x + 2y + 1) dx.

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  9. If the normal to the ellipse (x^(2))/9+(y^(2))/4=1 which is farthest f...

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  10. sum(n=0)^oo1/(n !)[sum(k=0)^n(k+1)int0^1 2^(-(k+1)x)dx]

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  11. Consider the family of circles x^2 + y^2= r^2 2 lt r lt 5. If in the f...

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  12. Let T1, T2 and be two tangents drawn from (-2, 0) onto the circle C:x^...

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  13. The equation of two equal sides AB and AC of an isosceies triangle ABC...

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  14. Find the equation of the largest circle with centre (1, 0) that can be...

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  15. Prove that the circle x^2 + y^2 -6y + 4 = 0 and the parabola y^(2) = x...

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  16. Find the equation of the ellipse whose foci are the points (1, 2) and ...

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  17. Let ABC and PQR be any two triangles in the same plane. Assume that th...

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  18. An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n ti...

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  19. Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...

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  20. log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2.

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