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If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqr...

If `y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")),` prove that `siny=tan^2x/2`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate: int(x^2)/((x^2+4)\ (x^2+9))dx

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  2. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4, then find the val...

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  3. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

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  4. Find the image of the point having position vector hat i+2 hat j+4 ha...

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  5. Find the equation of a plane which is at a distance of 3\ sqrt(3) unit...

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  6. Evaluate : int xsin^(-1)\ x\ \ dx

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  7. Evaluate : int(dx)/(sqrt(5-4x-2x^2))

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  8. Prove that the radius of the right circular cylinder of greatest cu...

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  9. The amount of pollution content added in air in a city due to x- diese...

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  10. An open box with a square base is to be made out of a given quantit...

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  11. Solve the following differential equation: (dy)/(dx)+ycotx=4x\ cos e c...

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  12. Find the particular solution of the differential equation: (1+e^(2x))d...

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  13. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  14. If vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k a...

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  15. Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[...

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  16. Consider f: R+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inv...

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  17. What are the direction cosines of a line, which makes equal angles ...

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  18. Evaluate: int(dx)/(x(x^5+3))

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  19. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

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  20. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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