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Prove that the determinant |[x,sintheta,...

Prove that the determinant `|[x,sintheta,costheta],[-sintheta,-x,1],[costheta,1,x]|`, is independent of `theta`

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Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

Prove that (sectheta+tantheta)(1-sintheta)=costheta .

Prove that sin^3theta+cos^3theta=(sintheta+costheta)(1-sinthetacostheta) .

Prove that sintheta(cosectheta-sintheta)=cos^2theta .

Prove that sintheta/(1+costheta)+sintheta/(1-costheta)=2/sintheta .

Evaluate |(2costheta,-2sintheta),(sintheta,costheta)|

Write the inverse of the matrix: {:[(costheta, sintheta),(-sintheta,costheta)]

Prove that (sintheta-2sin^3theta)/(2cos^3theta-costheta)=tantheta .

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

ACCURATE PUBLICATION-DETERMINANTS-(Question carrying 2 marks)
  1. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  2. If Delta=|{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}|"...

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  3. Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,...

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  4. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

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  5. If a, b, c are positive and unequal, show that value of the determinan...

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  6. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  7. Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2...

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  8. Prove that |{:((a+1)(a+2),a+2,1),((a+2)(a+3),a+3,1),((a+3)(a+4),a+4,1)...

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  9. Without expanding, prove the following |(a,a+b,a+2b),(a+2b,a,a+b),(...

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  10. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

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  11. Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b...

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  12. Without expanding, prove the following |(a,b-c,c-b),(a-c,b,c-a),(a-...

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  13. If a+b+c ne 0 and |{:(a,b,c),(b,c,a),(c,a,b):}|=0, then using properti...

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  14. Using the properties of determinants, prove that following : |{:(1,x...

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  15. If f(x) = {:|(a,-1,0),(ax,a,-1),(ax^2,ax,a)|, using properties of dete...

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  16. Show that triangle = |[(y+z)^2,xy,zx],[xy,(x+z)^2,yz],[xz,yz,(x+y)^2]|...

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  17. If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| and Delta(1)=|{:(1,...

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  18. Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1...

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  19. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

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  20. Find the equation of the line joining A(1,3) and B(0,0) using determin...

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