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Find the value of the following: tan [1...

Find the value of the following: `tan [1/2[sin^(-1) ((2x)/(1+x^2))+cos^(-1) ((1-y^2)/(1+y^2))]], |x|< 1, y > 0` and `x y < 1`.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the area of the greatest rectangle that can be inscribed in an...

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  2. If the binary operation **, defined on Q, is defined as a**b=2a+b-a ...

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  3. Find the value of the following: tan [1/2[sin^(-1) ((2x)/(1+x^2))+cos...

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  4. Evaluate : int0^1 1/(sqrt(2x+3))\ dx

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  5. Find a unit vector in the direction of vec a=2 hat i-\ 3 hat j+6 hat ...

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  6. If [[y+2x,5],[-x,3]]=[[7, 5],[-2 ,3]], find the value of y

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  7. Find the position vector of a point R which divides the line joinin...

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  9. What is the cosine of the angle which the vector sqrt(2) hat i+ hat j+...

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  10. On a multiple choice examination with three possible answers (out o...

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  11. If A=(a(i j))= [[2, 3,-5],[1, 4, 9],[ 0, 7,-2]] and B=(b(i j))=[[2, 1,...

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  12. Using elementary row operations, find the inverse of the following m...

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  13. Let Z be the set of all integers and R be the relation on Z defined as...

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  14. Evaluate : int(pi//6)^(pi//3)(sinx+cosx)/(sqrt(sin2x))\ dxdot

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  15. If siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  16. If (cosx)^y=(cosy)^x , find (dy)/(dx)

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  17. Evaluate: intx^2log(1+x)dx\

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

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  19. Prove that the volume of the largest cone, that can be inscribed in...

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  20. Show that the normal at any point theta to the curve x=acostheta+at...

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