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Prove the following: [[(b+c)^2,a^2,bc]...

Prove the following:
`[[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2,ab]]`
=`(a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
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  2. Show that the curves y = 2^(x) and y = 5^(x) intersect at an angle tan...

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  3. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  4. Find the inverse of the following matrix using elementary transformati...

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  5. If A is a singular matrix, then what is A(adjA)?

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  6. Give example of a function which is increasing in (-oo,2) and (3,oo) a...

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  7. If the direction angles of a line are alpha=30^@ and beta=60^@, find t...

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  8. Give an example of a relation which is not a function.

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  9. Write the integrating factor of the differential equation dy/dx(x+y+1)...

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  10. tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}.

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  11. What is the angle between vecaand vecb if abs(veca+vecb)=abs(veca-vecb...

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  12. If M=[(1,1,1),(1,1,1),(1,1,1)],then what is M^50 ?

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  13. Write the value x for which d/dxsin(sin^-1x)=1

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  14. What is the value of int(-1)^(1)ln(frac[4-x][4+x])dx?

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  15. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  16. Show that if R is an equivalence relation on X then dom R=rngR =X.

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  17. Solve graphically: Maximize Z=5x+6y subject to 2x+3yle6,x, yge0

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  18. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  19. Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine ...

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  20. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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