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Evaluate: int(cos2x-cos2alpha)/(cosx-cos...

Evaluate: `int(cos2x-cos2alpha)/(cosx-cosalpha)\ dxdot`

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To evaluate the integral \[ I = \int \frac{\cos(2x) - \cos(2\alpha)}{\cos(x) - \cos(\alpha)} \, dx \] we can follow these steps: ...
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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Write the direction cosines of a line parallel to z-axis.

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  2. If f(x)=(4x+3)/(6x-4) ,\ x\ !=2/3, show that fof(x)=x for all x!=2/3do...

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  3. Evaluate: int(cos2x-cos2alpha)/(cosx-cosalpha)\ dxdot

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  4. Evaluate : int(1-x^2)/(x(1-2x))\ dxdot

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  5. Evaluate: inte^x\ ((sin4x-4)/(1-cos4x))\ dx

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  6. Evaluate: int(x+2)/(sqrt(x^2+2x+3))dx

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  7. Differentiate x^(xcosx)+(x^2+1)/(x^2-1)\ wdotrdottdotx

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  8. If x=a\ (theta-sintheta),\ y=a\ (1+costheta),\ \ \ find (d^2\ y)/(dx^...

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  9. If the radius of a sphere is measured as 9 cm with an error of 0.03...

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  10. Prove that y=(4sintheta)/((2+costheta))-theta is an increasing func...

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  11. Evaluate: int(sinx+cosx)/(9+16sin2x)\ dx

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  12. Show that the total surface area of a closed cuboid with square bas...

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  13. Show that the height of the cylinder of maximum volume that can be ...

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  14. If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(d...

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  15. Prove that: d/(dx)[x/2\ sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)]=sqrt(a^2-...

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  16. Find the vector equation of the plane which contains the line of in...

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  17. Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2...

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  18. Show that the function f(x)=2x-|x| is continuous but not differenti...

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  19. Differentiate tan^(-1)((sqrt(1+x^2-1))/x) with respect to tan^(-1)x...

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  20. Let A = R × R and * be the binary operation on A defined by (a, b) ...

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