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If r^2 =x^2 +y^2+z^2, "Prove that" "tan...

If `r^2 =x^2 +y^2+z^2, "Prove that" `
`"tan"^(-1) (yz)/(xr) ="tan"^(-1) (zx)/(yr) +"tan"^(-1) (xy)/(zr) =pi/2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

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  2. Minimize:Z=6x1+7x2 "Subject to":x1+2x2 ge 4 x1,x2 ge 0

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  3. If r^2 =x^2 +y^2+z^2, "Prove that" "tan"^(-1) (yz)/(xr) ="tan"^(-1) (...

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  4. Find A^-1 if A=[(1,2),(3,5)] by using elementary row operations.

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  5. Evaluate [[1,a,bc],[1,b,ca],[1,c,ab]]-[[1,a,a^2],[1,b,b^2],[1,c,c^2]]

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  6. Define involuntary matrix and show that [(0,1,-1),(4,-3,4),(3,-3,4)] i...

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  7. If [(3,-2),(5,1)][(x),(y)]=[(12),(7)], then find xand y.

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  8. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  9. If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx)=sqrt...

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  10. If y = e^(m cos^(-1) x) (1-x^2)y2-xy1 = m^2y

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  11. Differentiate with respect to x: y=3^(x^2)+tan^-1((cosx+sinx)/(cosx-si...

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  12. Show that f(x)=x^3-6x^2+24x+4 has neither a maximum nor a minimum valu...

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  13. Find Integrating factor of:(x logx)dy/dx+y=2logx

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  14. Integrate int(x+7)/(x^2+8x)dx

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  15. Solve dy/dx+y/x=xy^2.

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  16. Prove that int(pi//6)^(pi//3)1/(1+sqrt(tanX))dx =(pi)/12

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  17. Prove that the measure of the angle between two main diagonals of a cu...

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  18. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  19. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  20. Show that the vector area of the triangle whosse vertices have positio...

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