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The maximum value of |(1,1,1),(1,1+sinth...

The maximum value of `|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|` is `1/2`

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Given,`|(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)|`
applying `c_1​=c_1​−c_2`​ and `c_2​=c_2​−c_3`
​`|(0,0,1),(-sintheta,sintheta,1),(0,-costheta,1+costheta)|`
=`1(sinθcosθ−0) sinθ cosθ`
=`(1/2)​.2sinθcosθ`
=`2sin2θ​`
...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Write the value of the determinant |[p, p+1],[p-1,p]| .

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  2. Write the value of |(x+y,y+z,z+x),(z,x,y),(-3,-3,-3)|

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  3. The maximum value of |(1,1,1),(1,1+sintheta,1),(1,1,1+costheta)| is 1/...

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  4. If x in N and |x+3-2-3x2x|=8, then find the value of xdot

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  5. If |xsinthetacostheta-sintheta-x1costheta1x|=8 , write the value of xd...

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  6. If Delta=|a(11)a(12)a(13)a(21)a(22)a(23)a(31)a(32)a(33)| and A(i j) is...

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  7. Which of the following is not correct in a given determinant of A , wh...

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  8. Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3...

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  9. The value of the determinant |a^2a1cosn xcos(n+a)xcos(n+2)xsinn xsin(n...

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  10. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

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  11. Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]| =a x^4+b x^3+c x^2+...

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  12. Using the factor theorem it is found that a+b , b+ca n dc+a are three ...

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  13. If a ,b ,c are different, then the value of |0x^2-a x^3-b x^2+a0x^2+c ...

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  14. If the determinant |[a ,b,2a alpha+3b],[b ,c, 2b alpha+3c],[2a alpha+3...

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  15. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

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

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  17. The value of /\=|[5^2, 5^3, 5^4],[ 5^3, 5^4, 5^5],[ 5^4, 5^5, 5^6]| is...

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  18. |(log)3 512(log)4 3(log)3 8(log)4 9|xx|(log)2 3(log)8 3(log)3 4(log)3 ...

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  19. If a, b, c, are in A.P, then the determinant|x+2x+3x+2a x+3x+4x+2b x+4...

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

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