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In triangle A B C , if |1 1 1cotA/2cotB/...

In triangle `A B C` , if `|1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tanA/2tanA/2+tanB/2|` then the triangle must be a. equilateral b. isosceles c. obtuse angled`` d. none of these

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CENGAGE-DETERMINANTS-All Questions
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  2. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  3. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

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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 " x(i) =a(i) b(i) C(i) i= 1,2,3 are three- digit positive integer...

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

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

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

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  10. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

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  11. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

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

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  13. Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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

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  15. If |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c) xx(x + a + b...

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  16. If a(1), a(2), a(3), ………, a(n)….. are in G.P., then the determinant De...

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  17. By using properties of determinants , show that : {:[( a^(2) + 1, a...

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

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  19. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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  20. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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