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In triangle A B C , if |[1, 1, 1],[cot(A...

In triangle `A B C` , if `|[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/2)+tan(C/2),tan(C/2)+tan(A/2),tan(A/2) +tan(B/2)]|`=0 then the triangle must be a. equilateral b. isosceles c. obtuse angled`` d. none of these

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  3. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

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  4. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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

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  6. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

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  7. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  8. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  9. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  10. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  12. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  13. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  15. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+b]...

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  16. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  17. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[log a...

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  18. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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  19. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

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  20. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

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