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Prove the following: tan^(-1)(1/4)+t...

Prove the following: `tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)`

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Prove that tan^(-1) (1/4) + tan^(-1) (2/9) = 1/2 sin^(-1) (4/5)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the inverse of the following matrix using elementary operations: ...

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  2. Using properties of determinants, prove the following: |[x,x^2,1+px^3]...

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  3. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

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  4. Solve the following for x : cos^(-1)((x^2 - 1)/(x^2 + 1))+t a n^(-1...

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  5. Using matrices, solve the following system of equations: x\ -\ y+z...

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  6. If A^(-1) =[(3,-1,1),(-15,6,-5),(5,-2,2)] and B = [(1,2,-2), (-1,3,0),...

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  7. A merchant plans to sell two types of personal computers — a deskto...

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  8. Given three identical boxes I, II and III each containing two coins...

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  9. Prove that: int0^(pi/4)(sqrt(tanx)+sqrt(cotx)\ dx=sqrt(2)dotpi/2

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  10. Find the shortest distance between the following lines whose vector...

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  11. Using vectors, find the area of the triangle with vertices A (1, 1,...

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  12. Using matrices, solve the following system of equations: 4x+3y+3z=6...

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  13. A random variable X has the following probability distribution: ...

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  14. A window has the shape of a rectangle surmounted by an equilateral ...

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  15. Find the distance of the point (-1,\ -5,\ -10) , from the point of int...

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  16. Show that the right-circular cone of least curved surface and given...

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  17. How many times must a man toss a fair coin, so that the probability...

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  18. Using elementary transformations, find the inverse of the matrix [[-1,...

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  19. Find the equation of the tangent to the curve y=sqrt(3x-2) which is...

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  20. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

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