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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 .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Solve for x":"|(a+x,a-x,a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0

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  2. Solve the equation |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)...

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  3. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

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  4. Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^...

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  5. Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b...

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

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  7. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

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  8. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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  9. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

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  10. Prove that : {:|(a^2a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b...

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  11. If p,q,r are not in G.P. and {:|(1,q/p,alpha+q/p),(1,r/q,alpha+r/q),...

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  12. Using determinant , find the area of triangle with verticles (1,0) ,...

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  13. Using determinants find the area of triangle with vertices (1,-1), ...

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  14. Find the area of the triangle with vertices at the points given in eac...

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  15. Find area of the triangle with vertices at the point given in the fol...

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  16. Find area of the triangle with vertices at the point given in the fol...

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  17. Using determinants, show that the following points are collinear: (1...

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  18. Using determinants, show that the following points are collinear: (-...

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  19. If the point (3,-2),(x,2),(8,8) are collinear, find 'x' using determin...

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  20. if area of triangle is 35sq.unit with vertices (2,-6) (5,4) and (K,4) ...

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