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If A+B+C=pi,then show that Abs((-1,cosC,...

If A+B+C=pi,then show that `Abs((-1,cosC,cosB),(cosC,-1,cosA),(cosB,cosA,-1))=0`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  2. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  3. If A+B+C=pi,then show that Abs((-1,cosC,cosB),(cosC,-1,cosA),(cosB,cos...

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  4. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  5. If A=[(1,2),(2,3),(3,4)]and B=[(2,3,0),(1,2,3)],then verify that (AB)^...

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  6. Find A^-1 if A=[(4,-1),(2,3)]

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  7. Express[(3,-1,0),(2,2,5),(1,3,2)]as sum of a symmetric and a skew symm...

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  8. Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...

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  9. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  10. Find the interval where f(x)=sinx,x in[0,2pi] increasing.

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  11. If siny=xcos(a+y),show that dy/dx=cos^2(a+y)/cosaand find the value of...

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  12. Determine the area of the region bounded by y^2=x^3 and the double ord...

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  13. int(xe^x)/(1+x^2)dx

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  14. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  15. Find the solution of the following differential equations: xdy/dx+sqrt...

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  16. int(pi//6)^(pi//3)dx/(1+sqrtcotx)

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  17. Prove the following by vector method. The diagonals of a rhombus are a...

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

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  19. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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

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