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If A+B+C =pi, show that |["sin"^(2)A,...

If A+B+C =`pi`, show that
`|["sin"^(2)A, "sin A cos A", "cos"^(2)A],["sin"^(2) B, "sin B cos B", "cos"^(2)B],["sin"^(2)C, "sin C cos C", "cos"^(2)C]| =-"sin (A-B)"sin"(B-C)"sin"(C-A)"`

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To show that \[ \begin{vmatrix} \sin^2 A & \sin A \cos A & \cos^2 A \\ \sin^2 B & \sin B \cos B & \cos^2 B \\ \sin^2 C & \sin C \cos C & \cos^2 C \end{vmatrix} = -\sin(A-B) \sin(B-C) \sin(C-A) ...
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RS AGGARWAL-DETERMINANTS-Objective Questions
  1. If A+B+C =pi, show that |["sin"^(2)A, "sin A cos A", "cos"^(2)A],["...

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  2. |["cos"70^(@), "sin"20^(@)], ["sin"70^(@), "cos"20^(@)]|=?

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  3. |["cos"15^(@), "sin"15^(@)], ["sin"15^(@), "cos"15^(@)]|=?

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  4. |["sin"23^(@), -"sin"7^(@)], ["cos"23^(@), "cos"7^(@)]|=?

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  5. Evaluate: |(a+i b, c+i d),(-c+i d, a-i b)|

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  6. Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| ...

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  7. If omega is a complex cube root of unity then the value of the determi...

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  8. If A=[[1^2,2^2,3^2],[2^2,3^2,4^2],[3^2,4^2,5^2]] then |AdjA|=

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  9. |(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)|=?

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  10. |[a-b, b-c, c-a], [b-c, c-a, a-b], [c-a, a-b, b-c]|=?

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  11. find |(1, 1+p,1+p+q),(2, 3+2p,1+3p+2q),(3, 6+3p, 1+6 p+3q)|=.

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  12. |{:(1, 1, 1),(a, b, c),(a^(3), b^(3), c^(3)):}|= is equal to

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  13. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

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  14. If a, b, c be distinct positive real numbers then the value of |[a, b,...

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  15. Q. |(x+y,x,x),(15x+4y,4x,2x),(10x +8y,8x,3x)|=x^3

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  16. Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

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  17. |[a, a+2b, a+2b+3c], [3a, 4a+6b, 5a+7b+9c], [6a, 9a+12b, 11a+15b+18c]|...

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  18. Prove that|[b+c,a,b],[c+a,c,a],[a+b,b,c]|=(a+b+c)(a-c)^2

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  19. |[1, 1, 1], [1, 1+x, 1], [1, 1, 1+y]|=?

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  20. |[bc, b+c, 1], [ca, c+a, 1], [ab, a+b, 1]|=?

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  21. |[b+c, a, a], [b, c+a, b], [c, c, a+b]|=?

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