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If A+B+C=pi, then the value of |[sin(...

If `A+B+C=pi,` then the value of `|[sin(A+B+C),sin(A+C),cosC],[-sinB,0,tanC],[cos(A+B),tan(B+C),0]|`is equal to (a)`0` (b) `1` (c) `2sinBtanAcosC` (d) none of these

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`|[sin(A+B+C),sin(A+C),cosC],[-sinB,0,tanC],[cos(A+B),tan(B+C),0]|`

=`|[sin pi,sinB,cosC],[-sinB,0,tanA],[cos(pi-C),-tanA,0]|`

=`|[0,sinB,cosC],[-sinB,0,tanA],[-cosC,-tanA,0]|`

`=-sinB(tanAcosC)+cosC(sinBtanA)=0`
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  2. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

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  3. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

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  4. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  15. Evaluate the determinant D=|2 3-2 1 2 3-2 1-3| by expanding it alon...

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  16. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by using Sarrus diagram.

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  17. Evaluate =|-1 6-2 2 1 1 4 1-3| by two methods.

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  18. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  19. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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