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Evaluate |(cosalphacosbeta,cosalpha sinb...

Evaluate `|(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|`

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  7. Prove that the value of each the following determinants is zero: |...

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  8. If |(b +c,c +a,a +b),(a +b,b +c,c +a),(c +a,a +b,b +c)| = k |(a,b,c),(...

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  9. A triangle has vertices Ai(xi , yi)fori=1,2,3 If the orthocentre of tr...

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  10. If alpha,beta,gamma are the roots of a x^3+b x^2+cx+d=0 and |[alpha,b...

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  12. Prove that the value of each the following determinants is zero: |[(a^...

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  14. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

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  15. Prove that the value of each the following determinants is zero: |[l...

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  17. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  18. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  19. Which of the following values of alpha satisfying the equation |(1+alp...

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  20. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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