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Prove the sin^2(sin^(-1) x+sin^(-1) y+s...

Prove the ` sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z)`
`=cos^2 (cos^(-1)x +cos^(-1) y+cos^(-1) z)`

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SHARAM PUBLICATION-MODEL QUESTION PAPER 14-EXERCISE
  1. What are the direction consines of the normal to the plane 3x - 2y - 2...

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  2. Let f : W rarr W be defined as f (x) = x -1 if x is odd and f(x) = x +...

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  3. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

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  4. Solve for x tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/79),x>0.

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  5. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  6. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

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  7. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

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  8. Prove that:|[1, a ,a^2],[a^2, 1 ,a],[a, a^2, 1]| is a perfect square.

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  9. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  10. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  11. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

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  12. Find the equation of tangent to the curve x^2 + 3y = 3 which is parall...

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  13. Find the extreme values of the function y = X + 1/x.

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  14. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

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  15. Integrate the following intsec^2sqrtx/sqrtxdx

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  16. intx^2tan^-1xdx

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  17. Solve (dy)/(dx)+y=e^(-x)

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  18. Using vector method find the area of the triangle with vertices (1, 0,...

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  19. Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...

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  20. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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